### Home > APCALC > Chapter 4 > Lesson 4.1.3 > Problem4-39

4-39.

Let $f ( x ) = \left\{ \begin{array} { l l } { 2 x ^ { 2 } - 4 \text { for } x \leq 3 } \\ { - 2 x - 5 \text { for } x > 3 } \end{array} \right.$.

1. What is$\lim\limits _ { x \rightarrow 3 ^ { + } } f ( x )$?

Notice that the boundary point is $x = 3$. Which piece is to the right of that boundary point?

$=\lim \limits_{x\rightarrow 3^{+}}-2x-5=-11$

2. What is$\lim\limits _ { x \rightarrow 3 ^ { - } } f ( x )$?

Which piece of $f\left(x\right)$ is to the left of the boundary point?

3. What do your results from parts (a) and (b) tell you about $f$?

Do not claim continuity (or discontinuity) without accounting for all three conditions.