### Home > CALC > Chapter 3 > Lesson 3.1.1 > Problem3-13

3-13.

Is the function graphed at right continuous at the following values of $x$? If not, explain which conditions of continuity fail.

$x = −4$, $−2$, $0$, and $2$

Now use the three conditions to test if the function is continuous at $x = −2$, $x = 0$ and $x = 2$.

Examine the graph at $x = −4$

Condition 1:

$\lim\limits_{x\rightarrow -4^{-}}f(x)=0; \ \lim\limits_{x\rightarrow -4^{+}}f(x)=0$

$\lim\limits_{x\rightarrow -4^{-}}f(x)=\lim\limits_{x\rightarrow -4^{+}}f(x).$ Therefore $\lim\limits_{x\rightarrow -4}f(x)$ exists.

Condition 2:

$f(-4) = 0$.
Therefore $f(−4)$ exists.

Condition 3:

$\lim\limits_{x\rightarrow -4}f(x)=f(-4).$

$f(x)$ is continuous at $x = −4$