Question

algebra
review passage
determine the period of the following trigonometric function.
question
$f(x) = 11\cos(x - 3\pi) - 18$
select a single answer
$t = 2\pi$
$t = 18$
$t = -3$
$t = 11$
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Explanation:

Step1: Recall cosine period property

The base function $\cos(x)$ has period $2\pi$.

Step2: Analyze horizontal shift effect

A horizontal shift $\cos(x - c)$ does not change the period of the cosine function.

Step3: Analyze amplitude/vertical shift effect

Scaling the amplitude ($11$) and vertical shift ($-18$) do not affect the period of the cosine function.

Step4: Confirm final period

Thus, the period of $f(x)=11\cos(x - 3\pi)-18$ is $2\pi$.

Answer:

$T=2\pi$