) Find a possible formula for the trigonometric function graphed below. Use x as the independent variable in your formula.

Question

Answer 1

(There are an infinite number of answers)

Since the function is positive a 0, choose the cosine function y = y=Acos(B(x−D))+C

Find the midline at y = -1. This means our A(mplitude) is 3 because Max = 2 and min = -4

The function completes one cycle as x varies from 0 to 4, so our period is 4

In our general form, the period = |2pi/B| so B = pi/2

The vertical shift is -1, to bring the x-axis down to the midline; C = -1

There is no phase shift; D = 0

We write y = 3cos(pi*x/2) -1