Phase Shift Worksheet with Answer Key

What's on the worksheet

1. For each graph, factor the coefficient of x out of the input.
   y = 3\sin\left(2x - \dfrac{\pi}{3}\right)y = -2\cos\left(4x + \pi\right)y = \cos\left(\dfrac{x}{4} - \dfrac{\pi}{2}\right)y = 5\sin\left(\dfrac{\pi x}{3} + \dfrac{\pi}{2}\right)y = \dfrac{1}{2}\sin\left(4x + 3\right)
2. Let y = (3x - 7 π4).
3. Sketch y = 3(2x - 2π3) on [0, 2π].
4. The graph of y = 3x is slid sideways, and the new graph is written as y = (3x - d) with 0 ≤ d < 2π.
5. Diego rewrites y = (π4 - 2x) as y = (-2(x + π8)) and says the graph is y = (-2x) slid π8 to the left.
6. A sailboat on a mooring rolls from side to side.