General Form of Sine and Cosine — Quiz

Question 7 • Precalculus

Which graph represents the function h of x is equal to 2 sine open paren x plus pi over 2 close paren minus 1 ?

Answer

Image with description On a coordinate plane, a function has a maximum of 1 and minimum of negative 3. It completes one period at 2 pi. It crosses the y-axis at (0, 1).

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

Image with description On a coordinate plane, a function has a maximum of 1 and minimum of negative 3. It completes one period at 2 pi. It crosses the y-axis at (0, negative 3).

Image with description On a coordinate plane, a function has a maximum of 1 and minimum of negative 1. It completes one period at 2 pi. It crosses the y-axis at (0, 1).

Explanation

The amplitude is 2 and the vertical shift is −1, so the maximum is −1 + 2 = 1 and the minimum is −1 − 2 = −3. Also, h(0) = 2 sin(π/2) − 1 = 1, and the period is 2π. These features match choice A, which has maximum 1, minimum −3, period 2π, and y-intercept (0, 1).

AI-written and checked against the verified answer.

More from this Course

Quiz

Quiz

Quiz