Explain how the graph of y = –2sin(x) – 1 differs from the parent function. Make sure to compare key points used for graphing.

Answer:

The graph is vertically stretched by a factor of 2, reflected over the x-axis, and shifted 1 unit down. The parent function has maximum 1, minimum −1, and amplitude 1, while the transformed graph has maximum 1, minimum −3, and amplitude 2. Its key points change from (0, 0), (π/2, 1), (π, 0), (3π/2, −1), (2π, 0) to (0, −1), (π/2, −3), (π, −1), (3π/2, 1), (2π, −1).