Question

Use the image to answer the question.

Three trigonometric waves are drawn on a coordinate plane with the x-axis ranging from negative pi to 2 pi in increments of pi over 2 and the y-axis ranging from negative 4 to 4 in increments of 1.
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Create a table of values to determine which is the correct graph of y=4sinx
.

(1 point)
Responses

Graph C
Graph C

Graph A
Graph A

Graph B
Graph B

It is not possible to determine which graph is the graph of y=4sinx
.

Answer 1

Graph C.

Reason: y = 4 sin x gives
- x = 0 → y = 0
- x = π/2 → y = 4
- x = π → y = 0
- x = 3π/2 → y = −4
- x = 2π → y = 0

Graph C is the one that passes through (0,0), (π/2,4), (π,0), (3π/2,−4), (2π,0), so it matches y = 4 sin x.