5
QuizMultiple Choice

Symmetry

Question 5 • 26/27 ALGEBRA II A

Which statement best describes how to determine whether f(x) = x3 + 5x + 1 is an even function?

Answer
A
Determine whether –(x3 + 5x + 1) is equivalent to x3 + 5x + 1.
B
Determine whether (–x)3 + 5(–x) + 1 is equivalent to x3 + 5x + 1.
C
Determine whether –x3 + 5x + 1 is equivalent to –(x3 + 5x + 1).
D
Determine whether (–x)3 + 5(–x) + 1 is equivalent to –(x3 + 5x + 1).

Explanation

To determine whether a function is even, check whether f(−x) is equal to f(x). Substituting −x into the function gives (−x)³ + 5(−x) + 1, which should be compared with x³ + 5x + 1. This is the test described by choice B.

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