Question

for which value(s) of a does g(x) approach a different number from the right side than it approaches from the left side? (select all that apply.)
-3
-2
-1
0
1
3
for which value(s) of a does g(x) increase or decrease without bound as x approaches a or for which value(s) of a is g(x) not defined? (select all that apply.)
-3
-2
-1
0
1

Explanation:

Step1: Analyze left - hand and right - hand limits

Examine the graph at each given x - value to see if the left - hand limit $\lim_{x
ightarrow a^{-}}g(x)$ and the right - hand limit $\lim_{x
ightarrow a^{+}}g(x)$ are different. At $x = 0$, as $x$ approaches $0$ from the left, $g(x)$ approaches a negative value, and as $x$ approaches $0$ from the right, $g(x)$ approaches a positive value. At $x = 1$, as $x$ approaches $1$ from the left, $g(x)$ approaches a lower value and as $x$ approaches $1$ from the right, $g(x)$ approaches a higher value.

Step2: Analyze discontinuities and unbounded behavior

Look for vertical asymptotes or points of non - definition. At $x=-2$, the function has a vertical asymptote, so $g(x)$ either increases or decreases without bound as $x$ approaches $-2$. At $x = 0$, the function has a break, and at $x = 1$, the function has a jump.

Answer:

For the first question: 0, 1
For the second question: -2, 0, 1