AP Precalculus: Periodic Functions

Practice: amplitude, period, phase shift, and contextual modeling

Name:

Date:

Class Period:

1. Graph y = 3 sin(2pix) for x from 0 to 2. Mark one full cycle.

2. Graph y = -2 cos(4t) for t from 0 to pi. Label peaks and troughs.

3. Sketch h(x) = -5 sin(x) + 2. Show midline and amplitude.

4. Sketch f(x) = 2 cos(pi*(x - 3)). Identify the phase shift and period.

5. A Ferris wheel has radius 20 m and center height 25 m. It completes one revolution every 40 seconds. If the rider starts at the lowest point, graph height over the first 80 seconds.