23
QuizMultiple Choice

Modeling with Trigonometric Expressions and Functions: Part One — Test

Question 23 • Precalculus

Consider the function y is equal to cosine of x Which change would increase the period by a factor of 3 ?

Answer
A
Multiply x by 1 third .
B
Multiply x by 3 .
C
Multiply cosine of x by 3 .
D
Multiply cosine of x by 1 third.

Explanation

The period of y = cos(x) is 2π. Replacing x with x/3 gives y = cos(x/3), whose period is 6π: the input must increase by 6π for x/3 to increase by 2π. Thus, multiplying x by 1/3 increases the period by a factor of 3. Multiplying the cosine output changes the graph’s height, not its period.

AI-written and checked against the verified answer.

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