### Home > APCALC > Chapter 2 > Lesson 2.3.3 > Problem2-130

2-130.

A function, $f$, is continuous for all real numbers. If $f(x) = \large\frac { x ^ { 2 } - 9 } { x + 3 }$ when $x\ne-3$, then what must $f(-3)$ equal? Write a piecewise-defined function that represents this situation.

After factoring, you will see that there is a hole (not a vertical asymptote) at $x=−3$.

While$f(−3)$ does not exist, the

$\lim\limits _{x\rightarrow -3}f(x)$

exist, and gives us the $y$-value of the hole.