Modeling with Trigonometric Expressions and Functions: Part One — Test

Question 16 • Precalculus

Suppose the function h of x is equal to sine x is translated 3 pi over 2 units left and 11 units down. Which graph represents the result?

Answer

Image with description On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It increases through the y-axis at (0, negative 11).

Image with description On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It crosses the y-axis at (0, negative 10).

Image with description On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It decreases through the y-axis at (0, negative 11).

Image with description On a coordinate plane, a function has a maximum of negative 10 and minimum of negative 12. It completes one period at 2 pi. It crosses the y-axis at (0, negative 12).

Explanation

Shifting sine 3π/2 units left gives y = sin(x + 3π/2), and shifting it 11 units down gives y = sin(x + 3π/2) − 11. At x = 0, the value is sin(3π/2) − 11 = −12, the minimum of the function. Its maximum is −10 and its period is 2π, matching the graph that meets the y-axis at (0, −12).

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