Question

Math

Posted 4 months ago

```
Consider the graph of function $g$. The dashed lines represent asymptotes.
Which limit expressions agree with the graph?
Choose all answers that apply:
A) $\lim _{x \rightarrow 3} g(x)=\infty$
В $\lim _{x \rightarrow 3^{-}} g(x)=\infty$
(c) $\lim _{x \rightarrow 3^{+}} g(x)=\infty$
```

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Answer from Sia

Posted 4 months ago

Solution by Steps

step 1

We need to determine which limit expressions agree with the graph of the function $g$. The graph shows that as $x$ approaches $3$, the function $g(x)$ approaches infinity from both the left and the right

step 2

The limit expression $A$ is $\lim _{x \rightarrow 3} g(x)=\infty$. This means that as $x$ approaches $3$ from either direction, $g(x)$ approaches infinity. This is consistent with the graph

step 3

The limit expression $B$ is $\lim _{x \rightarrow 3^{-}} g(x)=\infty$. This means that as $x$ approaches $3$ from the left, $g(x)$ approaches infinity. This is consistent with the graph

step 4

The limit expression $C$ is $\lim _{x \rightarrow 3^{+}} g(x)=\infty$. This means that as $x$ approaches $3$ from the right, $g(x)$ approaches infinity. This is consistent with the graph

Answer

A, B, C

Key Concept

Limit expressions and asymptotes

Explanation

The graph shows that as $x$ approaches $3$ from both the left and the right, $g(x)$ approaches infinity, which means all the given limit expressions are correct.

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