Precalculus
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# Is the function h(x) = x^3-5 even, odd or neither?

May 23, 2016

neither

#### Explanation:

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

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

Even functions are symmetrical about the y-axis.

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

Odd functions are symmetrical about the origin.

Test for even

f(-x)=(-x)^3-5=-x^3-5≠f(x)

Since f(x) ≠ f( -x) , then f(x) is not even.

Test for odd

-f(x)=-(x^3-5)=-x^3+5≠f(-x)

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

hence f(x) is neither even nor odd.
graph{x^3-5 [-20, 20, -10, 10]}

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