Question

How do you determine if `f(x) = 3x - 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 are symmetrical 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) = 3( -x) - 1 = -3x - 1 ≠ f(x)

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

Test for odd

`-f(x)=-(3x-1)=-3x+1≠ f(-x)`

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

Thus f(x) is neither even nor odd