Question

Math

Posted 3 months ago

```
Consider the graph of function $h$.
Which limit expressions agree with the graph?
Choose all answers that apply:
A $\lim _{x \rightarrow-4} h(x)=-2$
в $\lim _{x \rightarrow 0^{+}} h(x)=2$
c) $\lim _{x \rightarrow 4^{-}} h(x)=2$
D None of the above
```

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Answer from Sia

Posted 3 months ago

Solution by Steps

step 2

The graph shows that as $x$ approaches $-4$ from either direction, $h(x)$ approaches $-2$. Therefore, $\lim_{x \rightarrow -4} h(x) = -2$

step 3

Next, we observe that as $x$ approaches $0$ from the right ($0^+$), $h(x)$ approaches $6$, not $2$. Therefore, $\lim_{x \rightarrow 0^+} h(x) \neq 2$

step 4

Finally, as $x$ approaches $4$ from the left ($4^-$), the graph does not provide any information about $h(x)$ at $x = 4$. Therefore, $\lim_{x \rightarrow 4^-} h(x) \neq 2$

A

Key Concept

Limit of a function

Explanation

The limit of a function as $x$ approaches a certain value is the value that the function approaches as $x$ gets closer to that value.

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