Graphing Sine and Cosine Functions — Quiz

Question 2 • Precalculus

Which graph represents the function y is equal to 2 sine open paren 1 half x close paren ?

Answer

Image with description On a coordinate plane, a function has a maximum of 2 and minimum of negative 2. It completes one period at 8 pi. The curve crosses the y-axis at (0, 2).

Image with description On a coordinate plane, a function has a maximum of 2 and minimum of negative 2. It completes one period at 4 pi. The curve decreases through y-axis at (0, 0).

Image with description On a coordinate plane, a function has a maximum of 2 and minimum of negative 2. It completes one period at 8 pi. The curve crosses the y-axis at negative 2.

Image with description On a coordinate plane, a function has a maximum of 2 and minimum of negative 2. It completes one period at 4 pi. The curve increases through the y-axis at (0, 0).

Explanation

The coefficient 2 gives the sine function an amplitude of 2, so its maximum is 2 and its minimum is −2. The period is 2π divided by 1/2, which equals 4π. At x = 0, the function is 0, and the curve rises as x increases, so the matching graph is the one that increases through (0, 0) and has period 4π: choice D.

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