Question

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

Answer 1

neither even nor odd.

Explanation:

To determine if F(x) 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 half-turn symmetry about the origin.

Test for even

F( -x) = (-x) + 3 = -x + 3 ≠ F(x)

Since F(x) ≠ F( -x) , then F(x) is not even

Test for odd

`-F(x)=-(x+3)=-x-3≠F(-x)`

Since F( -x) ≠ - F(x) , then F(x) is not odd

Thus F(x) is neither even nor odd.
graph{x+3 [-10, 10, -5, 5]}