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

2-130.

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

After factoring, you will see that there is a hole (not a vertical asymptote) at $x = −3$. While $f\left(−3\right)$ does not exist, the exist, and gives us the $y$-value of the hole.