Question

How do you determine if `f(x) = 2x^5 - 3x^2 + 2` is an even or odd function?

Answer 1

Neither

Explanation:

To determine if a function is even/odd the following applies.

• If f(x) = f( -x) then f(x) is even , `AAx`

Even functions have symmetry about the y-axis.

• If f( -x) = - f(x) then f(x) is odd , `AAx`

Odd functions have symmetry about the origin.
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Test for even :

f( -x) `= 2(-x)^5 - 3(-x)^2 + 2 = -2x^5 - 3x^2 + 2`

since f(x) ≠ f( -x) , then f(x) is not even.
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Test for odd :

`-f(x) = -(2x^5 - 3x^2 + 2) = -2x^5 + 3x^2 - 2`

since -f(x) ≠ f( -x) , then f(x) is not odd.