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

2-97.

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

1. $f\left(-10\right)=20$

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: $f(x)=x^2+1$.

$\text{Also consider the even function: }f(x)=\frac{1}{x^{2}}$