Question

For which function is f(-x) = f(x)? (A) f(x) = sqaure root x(B) f(x) = 2x (C) f(x) = x^2 (D) f(x) = x^2 (E) f(x) = 2^x

Answer 1

This question is about functions transformation, specifically, reflection.

The given transformation is

$f(-x)=f(x)$

This means that the function won't change if we change its variable x to -x.

The only function that can have such characteristic is the quadratic function because all even powers will always give a positive number. For example

$(-2)^2=4$

So, the right answers here are C and D, because they are quadratic functions.