### Home > CALC > Chapter 2 > Lesson 2.2.4 > Problem2-97

2-97.

$f(x)$ is an even function such that $f(2) = 4$ and $f(10) = 20$. Which of the following must be true? Could be true? Must be false?

1. $f(−10) = 20$

1. $f(−2) = −4$

1. $f(0) = 0$

Even functions have reflective symmetry across the $y$-axis.

Definition of an even function: $f(a) = f(−a)$

Must all even functions go through the origin?
Consider the even function: $f(x) = x^2 + 1$.
Also consider the even function: $f(x)=\frac{1}{x^{2}}$