General Form of Sine and Cosine — Quiz

Question 8 • Precalculus

Which graph represents the function g of x is equal to 7 cosine x after a shift of 5 pi over 3 units to the right?

Answer

Image with description On a coordinate plane, a function has a maximum of 7 and minimum of negative 7. It completes one period at 2 pi. It decreases through the y-axis at (0, 4).

Image with description On a coordinate plane, a function has a maximum of 7 and minimum of negative 7. It completes one period at 2 pi. It crosses the y-axis at (0, 6).

Image with description On a coordinate plane, a function has a maximum of 7 and minimum of negative 7. It completes one period at 2 pi. It crosses the y-axis at (0, negative 6).

Image with description On a coordinate plane, a function has a maximum of 7 and minimum of negative 7. It completes one period at 2 pi. It increases through the y-axis at (0, 4).

Explanation

Shifting 7 cos x right by 5π/3 gives g(x) = 7 cos(x − 5π/3). At x = 0, g(0) = 7 cos(−5π/3) = 3.5, which is shown approximately as 4. The function is decreasing there, so the matching graph is the one that decreases through the y-axis near (0, 4).

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