Question

How do you determine if `f(x)= x^3 + 1` is an even or odd function?

Answer 1

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 have symmetry about the y-axis.

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

Odd functions have symmetry about the origin.

Test for even

`f(-x)=(-x)^3+1=-x^3+1 ≠f(x)`

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

Test for odd

`-f(x)=-(x^3+1)=-x^3-1≠f(-x)`

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

`rArrx^3+1" is neither even nor odd"`
graph{x^3+1 [-10, 10, -5, 5]}