Question

Math

Posted 2 months ago

```
Function $h$ is graphed.
Select all correct statements about $h$ at $x=-1$.
Choose all answers that apply:
A Both $\lim _{x \rightarrow-1^{+}} h(x)$ and $\lim _{x \rightarrow-1^{-}} h(x)$ exist
B $\lim _{x \rightarrow-1} h(x)$ exists
c $h$ is defined at $x=-1$
D $h$ is continuous at $x=-1$
E None of the above
```

Sign in to unlock the answer

Answer from Sia

Posted 2 months ago

Solution by Steps

step 2

To determine if $\lim_{x \to -1} h(x)$ exists, we need both one-sided limits to be equal. Since both one-sided limits approach -5, $\lim_{x \to -1} h(x) = -5$ exists

step 3

To determine if $h$ is defined at $x = -1$, we observe the graph. There is a hole at the point (-1, -5), indicating that $h(-1)$ is not defined

step 4

To determine if $h$ is continuous at $x = -1$, the function must be defined at $x = -1$ and the limit as $x$ approaches -1 must equal $h(-1)$. Since $h(-1)$ is not defined, $h$ is not continuous at $x = -1$

A

Key Concept

Existence of Limits

Explanation

For a limit to exist at a point, both one-sided limits must exist and be equal.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Upgrade to Asksia Pro

Join a AskSia's Pro Plan, and get 24/7 AI tutoring for your reviews, assignments, quizzes and exam preps.

Unlimited chat query usages

Strong algorithms that better know you

Early access to new release features

Study Other Question