Practice Test

Question 2 • Precalculus

Which graph represents y is equal to cosine of open paren 2 x minus pi close paren plus 5 ?

Answer

Image with description On a coordinate plane, a function has a maximum of 7 and minimum of 3. It completes one period at 2 pi. It crosses the y-axis at (0, 3).

Image with description On a coordinate plane, a function has a maximum of 6 and minimum of 4. It completes one period at pi. It crosses the y-axis at (0, 4).

Image with description On a coordinate plane, a function has a maximum of 7 and minimum of 3. It completes one period at 2 pi. It decreases through the y-axis at (0, 5).

Image with description On a coordinate plane, a function has a maximum of 6 and minimum of 4. It completes one period at pi. It decreases through the y-axis at (0, 5).

Explanation

The vertical shift of +5 gives a midline of y = 5, and the cosine’s amplitude of 1 gives a maximum of 6 and a minimum of 4. The coefficient 2 makes the period 2π ÷ 2 = π. At x = 0, y = cos(−π) + 5 = 4, so the graph crosses the y-axis at (0, 4), matching choice B.

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