CPM Homework Help : CALC Problem 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 $2$

Hint:

Step:

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

Answer:

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 $x = −4$