General Form of Sine and Cosine — Quiz

Question 10 • Precalculus

Which graph represents the function y is equal to sine of open paren 1 half x close paren after a shift of 3 units down?

Answer

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

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

Image with description On a coordinate plane, a function has a maximum of negative 2 and minimum of negative 4. It completes one period at pi. It increases through the y-axis at (0, negative 3).

Image with description On a coordinate plane, a function has a maximum of negative 2 and minimum of negative 4. It completes one period at 4 pi. It increases through the y-axis at (0, negative 3).

Explanation

The graph of y = sin(x/2) − 3 has amplitude 1 and midline y = −3, so its maximum is −2 and minimum is −4. Its period is 2π ÷ (1/2) = 4π. At x = 0, the function equals −3 and is increasing, so the graph that matches is the one described in choice D.

AI-written and checked against the verified answer.

Back to All Questions

More from this Course

Quiz

Quiz

Quiz