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All Textbook Solutions for College Algebra

Given this figure, specify the graphed set in a. words b.set-builder notation c.interval notation Given Figure 12, identify the domain and range using interval notation.Find the domain and range of f(x)=2x .Graph the following piecewise function. f(x)={x3ifx12if1x4xifx4 Why does the domain differ for different functions?How do we determine the domain of a function defined by an equation?Explain why the domain of f(x)=x3 is different from the domain of f(x)=x .When describing sets of numbers using interval notation, when do you use a parenthesis and when do you use a bracket?How do you graph a piecewise function?For the following exercises, find the domain of each function using interval notation. f(x)=2x(x1)(x2)For the following exercises, find the domain of each function using interval notation. f(x)=52x2 For the following exercises, find the domain of each function using interval notation. f(x)=3x2 For the following exercises, find the domain of each function using interval notation f(x)=362x For the following exercises, find the domain of each function using interval notation. f(x)=43x For the following exercises, find the domain of each function using interval notation. f(x)=x2+4 For the following exercises, find the domain of each function using interval notation. f(x)=12x3 For the following exercises, find the domain of each function using interval notation f(x)=x13 For the following exercises, find the domain of each function using interval notation f(x)=9x6 For the following exercises, find the domain of each function using interval notation. f(x)=3x+14x+2 For the following exercises, find the domain of each function using interval notation. f(x)=x+4x4 For the following exercises, find the domain of each function using interval notation. f(x)=x3x2+9x22 For the following exercises, find the domain of each function using interval notation. 18. f(x)=1x2x6 For the following exercises, find the domain of each function using interval notation. 19. f(x)=2x3250x22x15 For the following exercises, find the domain of each function using interval notation 20. f(x)=5x3 For the following exercises, find the domain of each function using interval notation. f(x)=2x+15x For the following exercises, find the domain of each function using interval notation. f(x)=x4x6 For the following exercises, find the domain of each function using interval notation f(x)=x6x4 For the following exercises, find the domain of each function using interval notation. f(x)=xx For the following exercises, find the domain of each function using interval notation f(x)=x29xx281 For the following exercises, find the domain of each function using interval notation. 26. Find the domain of the function f(x)=2x350x by: a. using algebra. b.graphing the function in the radicand and determining intervals on the x-axis for which the radicand is nonnegative.For the following exercises, write the domain and range of each function using interval notation.For the following exercises, write the domain and range of each function using interval notation.For the following exercises, write the domain and range of each function using interval notation.For the following exercises, write the domain and range of each function using interval notation.For the following exercises, write the domain and range of each function using interval notation.For the following exercises, write the domain and range of each function using interval notation.For the following exercises, write the domain and range of each function using interval notation.For the following exercises, write the domain and range of each function using interval notation.For the following exercises, write the domain and range of each function using interval notation.For the following exercises, write the domain and range of each function using interval notation.For the following exercises, write the domain and range of each function using interval notation.For the following exercises, sketch a graph of the piecewise function. Write the domain in interval notation. f(x)={x+1ifx22x3ifx2 For the following exercises, sketch a graph of the piecewise function. Write the domain in interval notation. f(x)={2x1ifx11+xifx1 For the following exercises, sketch a graph of the piecewise function. Write the domain in interval notation. f(x)={x+1ifx0x1ifx0 For the following exercises, sketch a graph of the piecewise function. Write the domain in interval notation. f(x)={3ifx0 xifx0 For the following exercises, sketch a graph of the piecewise function. Write the domain in interval notation. f(x)={ x 2ifx01xifx0 For the following exercises, sketch a graph of the piecewise function. Write the domain in interval notation. f(x)={ x 2ifx0x+2ifx0 For the following exercises, sketch a graph of the piecewise function. Write the domain in interval notation. f(x)={x+1ifx1 x 3ifx1 For the following exercises, sketch a graph of the piecewise function. Write the domain in interval notation. f(x)={xifx21ifx2 For the following exercises, given each function f, evaluate f(3),f(2),f(1)andf(0) . 46. f(x)={x+1ifx22x3ifx2 For the following exercises, given each function f, evaluate f(3),f(2),f(1),andf(0) . 47. f(x)={xifx30ifx3 For the following exercises, given each function f, evaluate f(3),f(2),f(1),andf(0) . 48. f(x)={2x2+3ifx15x7ifx1 For the following exercises, given each function f, evaluate f(3),f(2),f(1),andf(0) . 49. f(x)={7x+3ifx07x+6ifx0 For the following exercises, given each function f, evaluate f(1),f(0),f(2),andf(4) . 50. f(x)={x22ifx24+x5ifx2 For the following exercises, given each function f, evaluate f(3),f(2),f(1),andf(0) . 51. f(x)={5xifx03if0x3x2ifx3 For the following exercises, write the domain for the piecewise function in interval notation. f(x)={x+1ifx22x3ifx2 For the following exercises, write the domain for the piecewise function in interval notation. 53. f(x)={x22ifx1x2+2ifx1 For the following exercises, write the domain for the piecewise function in interval notation. 54. f(x)={2x3ifx03x2+ifx2 Graph y=1x2 on the viewing window [0.5,0.1]and[0.1,0.5] . Determine the corresponding range for the viewing window. Show the graphs.Graph y=1x on the viewing window [0.5,0.1]and[0.1,0.5] . Determine the corresponding range for the viewing window. Show the graphs.Suppose the range of a function fis [5,8] . What is the range of |f(x)| ?Create a function in which the range is all nonnegative real numbers.Create a function in which the domain is x2 .The height h of a projectile is a function of the time t it is in die air. The height in feet for t seconds is given by the function h(t)=-16t2+96t . What is the domain of die function? What does the domain mean in the context of die problem?The cost in dollars of making x items is given by the function Cx)=10x+500. a. The fixed cost is determined when zero items are produced. Find the fixed cost for this item. b.What is the cost of making 25 items? c.Suppose the maximum cost allowed is SI500. What are the domain and range of the cost function, C(x) ?Using the data in Table 1 at the beginning of this section, find the average rate of change between 2005 and 2010.Find the average rate of change of f(x)=x2x on the interval [1,9] .Find the average rate of change of f(x)=x2+2x8 on the interval [5,a] in simplest forms in terms ofa.Graph the function f(x)=x36x215x+20 to estimate the local extrema of the function. Use these to determine the intervals on which the function is increasing and decreasing.Can the average rate of change of a function be constant?If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?How are the absolute maximum and minimum similar to and different from the local extrema?How does the graph of the absolute value function compare to the graph of the quadratic function, y=x2 , in terms of increasing and decreasing intervals?For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h in simplest form. f(x)=4x27on[1,b]For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h in simplest form. g(x)=2x29on[4,b]For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h in simplest form. p(x)=3x+4on[2,2+h]For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h in simplest form. 8. k(x)=4x2on[3,3+h]For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h in simplest form. f(x)=2x2+1on[x,x+h]For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h in simplest form. g(x)=3x22on[x,x+h]For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h in simplest form. a(t)=1t+4on[9,9+h]For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h in simplest form. b(x)=1x+3on[1,1+h]For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h in simplest form. 13. j(x)=3x3on[1,1+h]For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h in simplest form. 14. r(t)=4t3on[2,2+h]For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h in simplest form. 15. f(x+h)f(x)h given f(x)=2x23xon[x,x+h]For the following exercises, consider the graph of fshown in Figure 15. 16.Estimate the average rate of change from x=1tox=4 .For the following exercises, consider the graph of f shown in Figure 15. 17.Estimate the average rate of change from x=2tox=5 .For the following exercises, use the graph of each function to estimate the intervals on which the function is increasing or decreasing.For the following exercises, use the graph of each function to estimate the intervals on which the function is increasing or decreasing.For the following exercises, use the graph of each function to estimate the intervals on which the function is increasing or decreasing.For the following exercises, use the graph of each function to estimate the intervals on which the function is increasing or decreasing.For the following exercises, consider the graph shown in Figure 16. Estimate the intervals where the function is increasing or decreasing.For the following exercises, consider the graph shown in Figure 16. Estimate the point(s) at which the graph of f has a local maximum or a local minimum.For the following exercises, consider the graph in Figure 17. 24. If the complete graph of the function is shown, estimate the intervals where the function is increasing or decreasing.For the following exercises, consider the graph in Figure 17. 25. If the complete graph of the function is shown, estimate the absolute maximum and absolute minimum.Table 3 gives the annual sales (in millions of dollars) of a product from 1998 to 20006. What was the average rate of change of annual sales (a) between 2001 and 2002, and (b) between 2001 and 2004?Table 4 gives the population of a town (in thousand) from 2000 to 2008. What was the average rate of change of population (a) between 2002 and 2004, and (b) between 2002 and 2006?For the following exercises, find the average rate of change of each function on the interval specified f(x)=x2on[1,5]xFor the following exercises, find the average rate of change of each function on the interval specified h(x)=52x2on[2,4]For the following exercises, find the average rate of change of each function on the interval specified. q(x)=x3on[4,2]For the following exercises, find the average rate of change of each function on the interval specified. 31. g(x)=3x31on[-3,3]For the following exercises, find the average rate of change of each function on the interval specified. y=1x on [1,3]For the following exercises, find the average rate of change of each function on the interval specified. 33p(t)=(t24)(t+1)t2+3on[-3,1]For the following exercises, find the average rate of change of each function on the interval specified. 34. k(t)=6t2+4t3on[1,3]For the following exercises, use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function is increasing and decreasing. f(x)=x44x3+5 For the following exercises, use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function is increasing and decreasing. h(x)=x5+5x4+10x3+10x21 For the following exercises, use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function is increasing and decreasing. g(t)=tt+3 For the following exercises, use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function is increasing and decreasing. k(t)=3t23t For the following exercises, use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function is increasing and decreasing. s m(x)=x4+2x312x210x+4 For the following exercises, use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function is increasing and decreasing. n(x)=x48x3+18x26x+2 The graph of the functionfis shown in Figure 18. Based on the calculator screen shot, the point (1.333, 5.185) is which of the following? a. a relative (local) maximum of the function b.the vertex of the function c.the absolute maximum of the function d.a zero of the function Let f(x)=1x . Find a number c such that the average rate of change of the functionfon the interval (1,c) is 14 Let f(x)=1x . Find the number b such that the average rate of change off on the interval (2,b) is 110 .At the start of a trip, the odometer on a car read 21,395. At the end of the trip, 13.5 hours later, the odometer read 22,125, Assume the scale on the odometer is in miles. What is the average speed the car traveled during this trip?A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.m. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 10.7 gallons. What is the average rate of flow of the gasoline into the gas tank?Near the surface of the moon, the distance that an object falls is a function of time. It is given by d(t)=2.6667t2 , where t is in seconds and d(t) is in feet. If an object is dropped from a certain height, find the average velocity of die object from t=1tot=2 .The graph in Figure 19 illustrates the decay of a radioactive substance over t days. Use the graph to estimate the average decay rate from t=5tot=15 .Find and simplify the functions (fg)(x) and (fg)(x) . f(x)=x1 and g(x)=x21 Are they the same function?The gravitational force on a planet a distance r from the sun is given by the function G(r) . The acceleration of a planet subjected to any force F is given by the function a(F) . Form a meaningful composition of these two functions, and explain what it means.Using Table 1, evaluate f(g(1))andg(f(4)) .Using Figure 1, evaluate g(f(2)) .Given f(t)=t2tandh(x)=3x+2 , evaluate a.h(f(2)) b.h(f(2))Find the domain of (fg)(x) where f(x)=1x2 and g(x)=x+4 Write f(x)=434+x2 as the composition of two functions.How does one find the domain of the quotient of two functions, fg ?What is the composition of two functions, fg ?If the order is reversed when composing two functions, can the result ever be the same as the answer in the original order of the composition? If yes, give an example. If no, explain why not.How do you find the domain for the composition of two functions, fg ?For the following exercises, determine the domain for each function in interval notation 5. Given f(x)=x2+2x and g(x)=6x2 , find f+g , fg,fg,andfg .For the following exercises, determine the domain for each function in interval notation 6. Given f(x)=3x2+x and g(x)=5,f+g, fg,fg,andfg .For the following exercises, determine the domain for each function in interval notation 7. Given f(x)=2x2+4x and g(x)=12x, f+g, fg,fg,andfg .For the following exercises, determine the domain for each function in interval notation 8. Given f(x)=1x4 and g(x)=16x,f+g, fg,fg,andfg .For the following exercises, determine the domain for each function in interval notation 9. Given f(x)=3x2 and g(x)=x5,f+g, fg,fg,andfg .For the following exercises, determine the domain for each function in interval notation Given f(x)=x and g(x)=x3, findgf .For the following exercises, determine the domain for each function in interval notation 11. For the following exercises, find the indicated function given f(x)=2x2+1andg(x)=3x5 . a. f(g(2)) b. f(g(x)) c. g(f(x)) d. (gg)(x) e. (ff)(2)For the following exercises, use each pair of functions to find f(g(x)) and g(f(x)) . Simplify your answers. f(x)=x2+1,g(x)=x+2 For the following exercises, use each pair of functions to find f(g(x)) and g(f(x)) . Simplify your answers. f(x)=x+2,g(x)=x2+3 For the following exercises, use each pair of functions to find f(g(x)) and g(f(x)) . Simplify your answers. f(x)=x,g(x)=5x+1 For the following exercises, use each pair of functions to find f(g(x)) and g(f(x)) . Simplify your answers. 15. f(x)=x3,g(x)=x+1x3 For the following exercises, use each pair of functions to find f(g(x)) and g(f(x)) . Simplify your answers. f(x)=1x6,g(x)=7x+6 For the following exercises, use each pair of functions to find f(g(x)) and g(f(x)) . Simplify your answers. f(x)=1x4,g(x)=2x+4 For the following exercises, use each pair of functions to find f(g(x)) and g(f(x)) . Simplify your answers. f(x)=x4+6,g(x)=x6 and h(x)=x For the following exercises, use each pair of functions to find f(g(x)) and g(f(x)) . Simplify your answers. f(x)=x2+1,g(x)=1x , and h(x)=x+3 For the following exercises, use each set of functions to find f(g(h(x))) . Simplify your answers. 20.Given f(x)=1x , and g(x)=x3 , find the following: a. (fg)(x) b. the domain of (fg)(x) in interval notation c. (gf)(x) d. the domain of (gf)(x) e. (fg)x For the following exercises, use each set of functions to find f(g(h(x))) . Simplify your answers. 21. Given f(x)=24x and g(x)=3x , find the following: a. (gf)(x) b. the domain of (gf)(x) in interval notation For the following exercises, use each set of functions to find f(g(h(x))) . Simplify your answers. 22. Given the functions f(x)=1xx and g(x)=11+x2 , find the following: a. (gf)(x) b. (gf)(2)For the following exercises, use each set of functions to find f(g(h(x))) . Simplify your answers. 23. Given functions, p(x)=1x and m(x)=x24 , state the domain of each of the following functions using interval notation: a. p(x)m(x) b. p(m(x)) c. m(p(x))For the following exercises, use each set of functions to find f(g(h(x))) . Simplify your answers. 24. Given functions q(x)=1x and h(x)=x29 , state the domain of each of the following functions using interval notation. a. q(x)h(x) b. q(h(x)) c. h(q(x))For the following exercises, use each set of functions to find f(g(h(x))) . Simplify your answers. 25. For f(x)=1x and g(x)=x1 , write the domain of (fg)(x) in interval notation.For the following exercises, find functions f(x)andg(x) so the given function can be expressed as h(x)=f(g(x)) . 26. h(x)=(x+2)2 For the following exercises, find functions f(x)andg(x) so the given function can be expressed as h(x)=f(g(x)) . 27. h(x)=(x5)3 For the following exercises, find functions f(x)andg(x) so the given function can be expressed as h(x)=f(g(x)) . 28. h(x)=3x5 For the following exercises, find functions f(x)andg(x) so the given function can be expressed as h(x)=f(g(x)) . 29. h(x)=4(x+2)2 For the following exercises, find functions f(x)andg(x) so the given function can be expressed as h(x)=f(g(x)) . 30. h(x)=4+x3 For the following exercises, find functions f(x)andg(x) so the given function can be expressed as h(x)=f(g(x)) . 31. h(x)=12x33 For the following exercises, find functions f(x)andg(x) so the given function can be expressed as h(x)=f(g(x)) . 32. h(x)=1(3x24)3 For the following exercises, find functions f(x)andg(x) so the given function can be expressed as h(x)=f(g(x)) . 33. h(x)=3x2x+54 For the following exercises, find functions f(x)andg(x) so the given function can be expressed as h(x)=f(g(x)) . 34. h(x)=(8+x38x3)4 For the following exercises, find functions f(x)andg(x) so the given function can be expressed as h(x)=f(g(x)) . 35. h(x)=2x+6 For the following exercises, find functions f(x)andg(x) so the given function can be expressed as h(x)=f(g(x)) . 36. h(x)=(5x1)3 For the following exercises, find functions f(x)andg(x) so the given function can be expressed as h(x)=f(g(x)) . 37. h(x)=x13 For the following exercises, find functions f(x)andg(x) so the given function can be expressed as h(x)=f(g(x)) . 38. h(x)=x2+7 For the following exercises, find functions f(x)andg(x) so the given function can be expressed as h(x)=f(g(x)) . 39. h(x)=1(x2)3 For the following exercises, find functions f(x)andg(x) so the given function can be expressed as h(x)=f(g(x)) . 40. h(x)=(12x3)2 For the following exercises, find functions f(x)andg(x) so the given function can be expressed as h(x)=f(g(x)) . 41. h(x)=2x13x+4 For the following exercises, use the graph of f, shown in Figure 4, and g, shown in Figure 5, to evaluate the expressions. 42. f(g(3))For the following exercises, use the graph of f, shown in Figure 4, and g, shown in Figure 5, to evaluate the expressions. 43. f(g(1))For the following exercises, use the graph of f, shown in Figure 4, and g, shown inFigure 5, to evaluate the expressions. 44. f(g(1))For the following exercises, use the graph of f, shown in Figure 4, and g, shown in Figure 5, to evaluate the expressions. 45. f(g(0))For the following exercises, use the graph of f, shown in Figure 4, and g, shown in Figure 5, to evaluate the expressions. 46. f(g(5))For the following exercises, use the graph of f, shown in Figure 4, and g, shown in Figure 5, to evaluate the expressions. 47. f(g(4))For the following exercises, use the graph of f, shown in Figure 4, and g, shown in Figure 5, to evaluate the expressions. 48. f(g(2))For the following exercises, use the graph of f, shown in Figure 4, and g, shown in Figure 5, to evaluate the expressions. 49. g(g(0))For the following exercises, use the graph of f(x), shown in Figure 6,g(x), shown in Figure 7, and h(x), shown in Figure 8, to evaluate the expressions. 50. g(f(1))For the following exercises, use the graph of f(x), shown in Figure 6, g(x), shown in Figure 7, and h(x), shown in Figure 8, to evaluate the expressions. 51. g(f(2))For the following exercises, use the graph of f(x), shown in Figure 6, g(x), shown in Figure 7, and h(x), shown in Figure 8, to evaluate the expressions. 52. f(g(4))For the following exercises, use the graph of f(x), shown in Figure 6, g(x), shown in Figure 7, and h(x), shown in Figure 8, to evaluate the expressions. 53. f(g(1))For the following exercises, use the graph of f(x), shown in Figure 6, g(x), shown in Figure 7, and h(x), shown in Figure 8, to evaluate the expressions. 54. g(h(2))For the following exercises, use the graph of f(x), shown in Figure 6, g(x), shown in Figure 7, and h(x), shown in Figure 8, to evaluate the expressions. 55. h(f(2))For the following exercises, use the graph of f(x), shown in Figure 6, g(x), shown in Figure 7, and h(x), shown in Figure 8, to evaluate the expressions. 56. f(g(h(4)))For the following exercises, use the graph of f(x), shown in Figure 6, g(x), shown in Figure 7, and h(x), shown in Figure 8, to evaluate the expressions. 57. f(g(f(2)))For the following exercises, use the function values for f and g shown in Table 3 to evaluate each expression. 58. f(g(8))For the following exercises, use the function values for f and g shown in Table 3 to evaluate each expression. 59. f(g(5))For the following exercises, use the function values for f and g shown in Table 3 to evaluate each expression. 60. g(f(5))For the following exercises, use the function values for f and g shown in Table 3 to evaluate each expression. 61. g(f(3))For the following exercises, use the function values for f and g shown in Table 3 to evaluate each expression. 62. f(f(4))For the following exercises, use the function values for f and g shown in Table 3 to evaluate each expression. 63. f(f(1))For the following exercises, use the function values for f and g shown in Table 3 to evaluate each expression. 64. g(g(2))For the following exercises, use the function values for f and g shown in Table 3 to evaluate each expression. 65. g(g(6))For the following exercises, use the function values for f and g shown in Table 4 to evaluate each expression. 66. (fg)(1)For the following exercises, use the function values for f and g shown in Table 4 to evaluate each expression. 67. (fg)(2)For the following exercises, use the function values for f and g shown in Table 4 to evaluate each expression. 68. (gf)(2)For the following exercises, use the function values for f and g shown in Table 4 to evaluate each expression. 69. (gf)(3)For the following exercises, use the function values for f and g shown in Table 4 to evaluate each expression. 70. (gg)(1)For the following exercises, use the function values for f and g shown in Table 4 to evaluate each expression. 71. (ff)(3)For the following exercises, use each pair of functions to find f(g(0))andg(f(0)) . 72. f(x)=4x+8,g(x)=7x2 For the following exercises, use each pair of functions to find f(g(0))andg(f(0)) . 73. f(x)=5x+7,g(x)=42x2 For the following exercises, use each pair of functions to find f(g(0))andg(f(0)) . 74. f(x)=x+4,g(x)=12x3 For the following exercises, use each pair of functions to find f(g(0))andg(f(0)) . 75. f(x)=1x+2,g(x)=4x+3 For the following exercises, use the functions f(x)=2x2+1 and f(x)=3x+5 to evaluate or find the composite function as indicated. f(g(2))For the following exercises, use the functions f(x)=2x2+1 and f(x)=3x+5 to evaluate or find the composite function as indicated. f(g(x))For the following exercises, use the functions f(x)=2x2+1 and f(x)=3x+5 to evaluate or find the composite function as indicated. g(f(3))For the following exercises, use the functions f(x)=2x2+1 and f(x)=3x+5 to evaluate or find the composite function as indicated. (gg)(x)For the following exercises, use f(x)=x3+1 and g(x)=x13 . Find (fg)(x) and (gf)(x) . Compare the two answers.For the following exercises, use f(x)=x3+1 and g(x)=x13 . Find (fg)(2) and (gf)(2) .For the following exercises, use f(x)=x3+1 and g(x)=x13 . What is the domain of (gf)(x) ?For the following exercises, use f(x)=x3+1 and g(x)=x13 . What is the domain of (fg)(x) ?For the following exercises, use f(x)=x3+1 and g(x)=x13 . Let f(x)=1x . a. Find (ff)(x) . b. Is (ff)(x) for any function f the same result as the answer to part (a) for any function? Explain.For the following exercises, let F(x)=(x+1)5,f(x)=x5,andg(x)=x+1 . 85. True or False: (gf)(x)=F(x) .For the following exercises, let F(x)=(x+1)5,f(x)=x5,andg(x)=x+1 . 86. True or False: (fg)(x)=F(x) .For the following exercises, Find the composition when f(x)=x2+2 for all x0 and g(x)=x2 . 87. (fg)(6);(gf)(6)For the following exercises, Find the composition when f(x)=x2+2 for all x0 and g(x)=x2 . 88. (gf)(a);(fg)(a)For the following exercises, Find the composition when f(x)=x2+2 for all x0 and g(x)=x2 . 89. (fg)(11);(gf)(11)The function D(p) gives the number of items that will be demanded when the price is p. The production cost C(x) is the cost of producing x items. To determine the cost of production when the price is $6, you would do which of die following? a. Evaluate D(C(6)) . b. Evaluate C(D(6)) . c. Solve D(C(x))=6 . d.Solve C(D(p))=6 .The function A(d) gives the pain level on a scale of 0 to 10 experienced by a patient with d milligrams of a pain- reducing drug in her system.The milligrams of the drug in the patient’s system after t minutes is modeled by m(t) . Which of the following would you do in order to determine when the patient will be at a pain level of 4? a. Evaluate A(m(4)) . b. Evaluate m(A(4)) . c. Solve A(m(t))=4 . d. Solve m(A(d))=4 .A store offers customers a 30% discount on the price x of selected items. Then, the store takes off an additional 15% at the cash register. Write a price function P(x) that computes the final price of the item in terms of the original price x. (Hint: Use function composition to find your answer.)A rain drop hitting a lake makes a circular ripple. If the radius, in inches, grows as a function of time in minutes according to r(t)=25t+2 , find the area of the ripple as a function of time. Find the area of the ripple at t=2 .A forest fire leaves behind an area of grass burned in an expanding circular pattern. If the radius of the circle of burning grass is increasing with time according to the formula r(t)=2t+1 , express the area burned as a function of time, t (minutes).Use the function you found in the previous exercise to find the total area burned after 5 minutes.The radius r, in inches, of a spherical balloon isrelated to the volume, V, by r(V)=3V43 . Air is pumped into the balloon, so the volume after t seconds is given by V(t)=10+20t . a. Find the composite function r(V(t)) . b.Find the exact time when the radius reaches 10 inches.The number of bacteria in a refrigerated food product is given by N(T)=23T256T+1,3T33 ,where T is the temperature of the food. When the food is removed from the refrigerator, the temperature is given by T(t)=5t+1.5 , where t is the time in hours. a. Find the composite function N(T(t)) . b. Find the time (round to two decimal places) when the bacteria count reaches 6,752.The function h(t)=4.9t2+30t gives the height h of a ball (in meters) thrown upward from the ground after t seconds. Suppose the ball was instead thrown from the top of a 10-m building. Relate this new height function b(t)toh(t) , and then find a formula for b(t) .Given the function f(x)=x , graph the original function f(x) and the transformation g(x)=f(x+2) on the same axes. Is this a horizontal or a vertical shift? Which way is the graph shifted and by how many units?Given f(x)=|x| , sketch a graph of h(x)=f(x-2)+4 .Write a formula for a transformation of the toolkit reciprocal function f(x)=1x that shifts the function’s graph one unit to the right and one unit up.Reflect the graph of f(x)=|x1| a. vertically and b. horizontally.A function f(x) is given as Table 9. Create a table for the functions below. g(x)=f(x) h(x)=f(x)Given the toolkit function f(x)=x2 , graph g(x)=-f(x)andh(x)=f(x) . Take note of any surprising behavior for these functions.Is the function f(s)=s4+3s2+7 even, odd, or neither?A function f is given as Table 12. Create a table for the function g(x)=34f(x) .Write the formula for the function that we get when we stretch the identity toolkit function by a factor of 3, and then shift it down by 2 units.Write a formula for the toolkit square root function horizontally stretched by a factor of 3.When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal shift from a vertical shift?When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal stretch from a vertical stretch?When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal compression from a vertical compression?When examining the formula of a function that is the result of multiple transformations, how can you tell a reflection with respect to the x-axis from a reflection with respect to the y-axis?How can you determine whether a function is odd or even from the formula of the function?For the following exercises, write a formula for the function obtained when the graph is shifted as described. 6. f(x)=x is shifted up 1 unit and to the left 2 units.For the following exercises, write a formula for the function obtained when the graph is shifted as described. 7. f(x)=|x| is shifted down 3 units and to the right 1 unit.For the following exercises, write a formula for the function obtained when the graph is shifted as described. f(x)=1x is shifted down 4 units and to the right 3 units.For the following exercises, write a formula for the function obtained when the graph is shifted as described. f(x)=1x2 is shifted up 2 units and to the left 4 units.For the following exercises, describe how the graph of the function is a transformation of the graph of the original function f. . y=f(x49)For the following exercises, describe how the graph of the function is a transformation of the graph of the original function f. y=f(x+43)For the following exercises, describe how the graph of the function is a transformation of the graph of the original function f. y=f(x+3)For the following exercises, describe how the graph of the function is a transformation of the graph of the original function f. y=f(x4)For the following exercises, describe how the graph of the function is a transformation of the graph of the original function f. y=f(x)+5 For the following exercises, describe how the graph of the function is a transformation of the graph of the original function f. y=f(x)+8 For the following exercises, describe how the graph of the function is a transformation of the graph of the original function f. y=f(x)2 For the following exercises, describe how the graph of the function is a transformation of the graph of the original function f. y=f(x)7 For the following exercises, describe how the graph of the function is a transformation of the graph of the original function f. y=f(x2)+3 For the following exercises, describe how the graph of the function is a transformation of the graph of the original function f. y=f(x+4)1 For the following exercises, determine the interval(s) on which the function is increasing and decreasing. f(x)=4(x+1)25 For the following exercises, determine the interval(s) on which the function is increasing and decreasing. g(x)=5(x+3)22 For the following exercises, determine the interval(s) on which the function is increasing and decreasing. a(x)=x+4 For the following exercises, determine the interval(s) on which the function is increasing and decreasing. 23. k(x)=3x1 For the following exercises, use the graph of f(x)=2X shown in Figure 31 to sketch a graph of each transformation of f(x) . 24. g(x)=2x+1 For the following exercises, use the graph of f(x)=2X shown in Figure 31 to sketch a graph of each transformation of f(x) . 25. h(x)=2x3 For the following exercises, use the graph of f(x)=2X shown in Figure 31 to sketch a graph of each transformation of f(x) . 26. w(x)=2x1 For the following exercises, sketch a graph of the function as a transformation of the graph of one of the toolkit functions. f(x)=(t+1)23 For the following exercises, sketch a graph of the function as a transformation of the graph of one of the toolkit functions. h(x)=x1+4 For the following exercises, sketch a graph of the function as a transformation of the graph of one of the toolkit functions. 29. k(x)=(x2)31 For the following exercises, sketch a graph of the function as a transformation of the graph of one of the toolkit functions. m(t)=3+t+2 Tubular representations for the functions f, g and h are given below. Write g(x) and h(x) as transformations of f(x) .Tubular representations for the functions f, g and h are given below. Write g(x) and h(x) as transformations of f(x) .For the following exercises, write an equation for each graphed function by using transformation of the graphs of one of the toolkit functions.For the following exercises, write an equation for each graphed function by using transformation of the graphs of one of the toolkit functions.For the following exercises, write an equation for each graphed function by using transformation of the graphs of one of the toolkit functions.For the following exercises, write an equation for each graphed function by using transformation of the graphs of one of the toolkit functions.For the following exercises, write an equation for each graphed function by using transformation of the graphs of one of the toolkit functions.For the following exercises, write an equation for each graphed function by using transformation of the graphs of one of the toolkit functions.For the following exercises, write an equation for each graphed function by using transformation of the graphs of one of the toolkit functions.For the following exercises, write an equation for each graphed function by using transformation of the graphs of one of the toolkit functions.For the following exercises, use the graphs of transformations of the square root function to find a formula for each of the functions.For the following exercises, use the graphs of transformations of the square root function to find a formula for each of the functions.Y1yg For the following exercises, use the graphs of the transformed toolkit functions to write a formula for each of the resulting functions.For the following exercises, use the graphs of the transformed toolkit functions to write a formula for each of the resulting functions.For the following exercises, use the graphs of the transformed toolkit functions to write a formula for each of the resulting functions.For the following exercises, use the graphs of the transformed toolkit functions to write a formula for each of the resulting functions.For the following exercises, determine whether the function is odd, even, or neither. f(x)=3x4 For the following exercises, determine whether the function is odd, even, or neither. g(x)=x For the following exercises, determine whether the function is odd, even, or neither. h(x)=1x+3x For the following exercises, determine whether the function is odd, even, or neither. f(x)=(x2)2 For the following exercises, determine whether the function is odd, even, or neither. g(x)=2x4 For the following exercises, determine whether the function is odd, even, or neither. h(x)=2xx3 For the following exercises, describe how the graph of each function is a transformation of the graph of the original function f. 53. g(x)=f(x)For the following exercises, describe how the graph of each function is a transformation of the graph of the original function f. 54. g(x)=f(x)For the following exercises, describe how the graph of each function is a transformation of the graph of the original function f. 55. g(x)=4f(x)For the following exercises, describe how the graph of each function is a transformation of the graph of the original function f. 56. g(x)=6f(x)For the following exercises, describe how the graph of each function is a transformation of the graph of the original function f. 57. g(x)=f(5x)For the following exercises, describe how the graph of each function is a transformation of the graph of the original function f. 58. g(x)=f(2x)For the following exercises, describe how the graph of each function is a transformation of the graph of the original function f. 59. g(x)=f(13x)For the following exercises, describe how the graph of each function is a transformation of the graph of the original function f. 60. g(x)=f(15x)For the following exercises, describe how the graph of each function is a transformation of the graph of the original function f. 61. g(x)=3f(x)For the following exercises, describe how the graph of each function is a transformation of the graph of the original function f. 62. g(x)=f(3x)For the following exercises, write a formula for the function g that results when the graph of a given toolkit function is transformed as described. 63. The graph of f(x)=|x| is reflected over they-axis and horizontally compressed by a factor of 14 .For the following exercises, write a formula for the function g that results when the graph of a given toolkit function is transformed as described. 64. The graph of f(x)=x is reflected over the x-axis and horizontally stretched by a factor of 2.For the following exercises, write a formula for the function g that results when the graph of a given toolkit function is transformed as described. 65. The graph of f(x)=1x2 is vertically compressed by a factor of 13 , then shifted to the left 2 units and down 3 units.For the following exercises, write a formula for the function g that results when the graph of a given toolkit function is transformed as described. 66. The graph of f(x)=1x is vertically stretched by a factor of 8, then shifted to the right 4 units and up 2 units.For the following exercises, write a formula for the function g that results when the graph of a given toolkit function is transformed as described. 67. The graph of f(x)=x2 is vertically compressed by a factor of 12 , then shifted to the right 5 units and up 1 unit For the following exercises, write a formula for the function g that results when the graph of a given toolkit function is transformed as described. 68.The graph of f(x)=x2 is horizontally stretched by a factor of 3, then shifted to the left 4 units and down 3 units.For the following exercises, write a formula for the function g that results when the graph of a given toolkit function is transformed as described. 69. g(x)=4(x+1)25

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