Question

use the provided graph to find the indicated quantities, if they exist. if it does not exist, select \does not exist\. (description: piece - wise graph with 3 pieces. first piece falls from the second quadrant to the 3rd, low point with open dot at (-8, -6). a solid dot above that at (-8, -3). the graph rises to the 2nd quadrant and ends at (-2, 3) with a solid dot. the 2nd piece falls vertically asymptotic to the right of x = -2. it intersects the positive x - axis and rises and falls to (6, 2) with an open dot. the 3rd piece begins with a solid dot at (6, 5), rises and then falls intersecting the x - axis at 10 and continues to fall. ) a. $lim_{x
ightarrow - 8}f(x)=$ select b. $f(-8)=$ select c. $lim_{x
ightarrow0^{+}}f(x)=$ select d. $lim_{x
ightarrow6^{-}}f(x)=$ select

Explanation:

Step1: Recall limit definition

The limit as $x$ approaches a value is the value the function approaches as $x$ gets closer to that value. For $\lim_{x
ightarrow - 8}f(x)$, we check the left - hand and right - hand limits. As $x$ approaches $-8$ from both sides, the function approaches $-6$ (since the open - dot value is what the function is approaching). So $\lim_{x
ightarrow - 8}f(x)=-6$.

Step2: Find function value

$f(-8)$ is the actual value of the function at $x = - 8$. Since there is a solid dot at $(-8,-3)$, $f(-8)=-3$.

Step3: Analyze right - hand limit

For $\lim_{x
ightarrow0^{+}}f(x)$, we look at the part of the graph for $x>0$. As $x$ approaches $0$ from the right, the function value approaches $2$. So $\lim_{x
ightarrow0^{+}}f(x)=2$.

Step4: Analyze left - hand limit

For $\lim_{x
ightarrow6^{-}}f(x)$, we look at the part of the graph for $x < 6$. As $x$ approaches $6$ from the left, the function value approaches $2$. So $\lim_{x
ightarrow6^{-}}f(x)=2$.

Answer:

a. $-6$
b. $-3$
c. $2$
d. $2$