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QuizMultiple Choice

Symmetry

Question 1 • 26/27 ALGEBRA II A

If f(x) = (xm + 9)2, which statement about f(x) is true?

Answer
A
f(x) is an even function for all values of m.
B
f(x) is an even function for all even values of m.
C
f(x) is an odd function for all values of m.
D
f(x) is an odd function for all odd values of m.

Explanation

For an even value of m, (-x)^m = x^m. Therefore f(-x) = ((-x)^m + 9)^2 = (x^m + 9)^2 = f(x), which is the definition of an even function. So the true statement is that f(x) is even for all even values of m.

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