Question

How do you determine if `f(x)=7x^2 - 2x + 1` is an even or odd function?

Answer 1

neither

Explanation:

To determine wether 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)=7(-x)^2-2(-x)+1=7x^2+2x+1`

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

Test for odd

`-f(x)=-(7x^2-2x+1)=-7x^2+2x-1`

Since f( -x) ≠ - f(x) , then f(x) is not odd
graph{7x^2-2x+1 [-10, 10, -5, 5]}