Eileen is trying to test if the function f(x) = x2 + 2x + 5 is even, odd or neither. She produces the following work:f(– x) = (–x)2 + 2(–x) + 5 = x2 – 2x + 5What conclusion can she reach?

For a function to be even, f(−x) must equal f(x); for it to be odd, f(−x) must equal −f(x). Here f(−x) = x² − 2x + 5, which is not the same as f(x) = x² + 2x + 5 or −f(x) = −x² − 2x − 5. Therefore, f(x) is neither even nor odd, which is choice C.

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