Question

Math

Posted 6 months ago

```
The function $h$ is defined for all real numbers.
What is a reasonable estimate for $\lim _{x \rightarrow 0} h(x) ?$
Choose 1 answer:
(A) -5
(B) 4
(C) 5
(D) The limit doesn't exist
```

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Answer from Sia

Posted 6 months ago

Solution by Steps

step 2

From the graph, we observe that there is an open circle at $(0, -5)$ and a closed circle at $(0, 5)$

step 3

The open circle at $(0, -5)$ indicates that $h(0) = -5$ is not included in the function's value

step 4

The closed circle at $(0, 5)$ indicates that $h(0) = 5$ is the value of the function at $x = 0$

step 5

Therefore, the limit $\lim_{x \to 0} h(x)$ is determined by the value at the closed circle, which is $5$

C

Key Concept

Limit of a function

Explanation

The limit of a function as $x$ approaches a certain value is determined by the value the function approaches, which is indicated by the closed circle on the graph.

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