A pendulum is a weight attached to a fixed rod, as shown in the figures. Suppose that during an experiment, a pendulum moves back and forth in a periodic manner. At the beginning of the experiment, when the time is t=0 seconds, the pendulum is at a point halfway between its maximum and minimum distances from the wall, 3 m away from the wall (Figure 1) and moving away from the wall. The pendulum first reaches its maximum distance from the wall, 5 m from the wall, when t = 2 seconds (Figure 2). When t = 8 seconds, the pendulum is back to a point halfway between its maximum and minimum distances from the wall. The pendulum continues to move back and forth so that the distance between the pendulum and the wall over time can be modeled by a sinusoidal function. Let f(t) be the distance between the wall and the pendulum t seconds after the beginning of the experiment. (a) Graph the function y=f(t) that models the distance between the wall and the pendulum. 3 m + Figure 1: t = 0 • First choose the appropriate starting graph from the ones below. • Then transform it to make a graph that shows the distance between the wall and the pendulum from the experiment. * V & k र्फ क He f 5 m Figure 2: t = 2

A pendulum is a weight attached to a fixed rod, as shown in the figures. Suppose that during an experiment, a pendulum moves back and forth in a periodic manner. At the beginning of the experiment, when the time is t=0 seconds, the pendulum is at a point halfway between its maximum and minimum distances from the wall, 3 m away from the wall (Figure 1) and moving away from the wall. The pendulum first reaches its maximum distance from the wall, 5 m from the wall, when t = 2 seconds (Figure 2). When t = 8 seconds, the pendulum is back to a point halfway between its maximum and minimum distances from the wall. The pendulum continues to move back and forth so that the distance between the pendulum and the wall over time can be modeled by a sinusoidal function. Let f(t) be the distance between the wall and the pendulum t seconds after the beginning of the experiment. (a) Graph the function y=f(t) that models the distance between the wall and the pendulum. 3 m + Figure 1: t = 0 • First choose the appropriate starting graph from the ones below. • Then transform it to make a graph that shows the distance between the wall and the pendulum from the experiment. * V & k र्फ क He f 5 m Figure 2: t = 2