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

Q: 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

∻Solution by Steps∻ ‖ step 1 ⋮ To determine if $ \lim_{x \to -1^+} h(x) $ and $ \lim_{x \to -1^-} h(x) $ exist, we observe the graph. Both one-sided limits approach $ y = -5 $ as $ x $ approaches $ -1 $ from the right and left. Therefore, both limits exist. ‖ ‖ step 2 ⋮ To determine if $ \lim_{x \to -1} h(x) $ exists, we check if the one-sided limits are equal. Since $ \lim_{x \to -1^+} h(x) = -5 $ and $ \lim_{x \to -1^-} h(x) = -5 $, the two-sided limit $ \lim_{x \to -1} h(x) $ exists and is equal to $ -5 $. ‖ ‖ step 3 ⋮ To determine if $ h $ is defined at $ x = -1 $, we observe the graph. There is a hole at $ x = -1 $, indicating that $ h(-1) $ is not defined. ‖ ‖ step 4 ⋮ To determine if $ h $ is continuous at $ x = -1 $, we need $ h(-1) $ to be defined and $ \lim_{x \to -1} h(x) = h(-1) $. Since $ h(-1) $ is not defined, $ h $ is not continuous at $ x = -1 $. ‖ ∻[question number] Answer∻ ***A*** ∻Key Concept∻ ⚹Existence of Limits⚹ ∻Explanation∻ ⚹For a limit to exist at a point, the left-hand limit and right-hand limit must both exist and be equal.⚹◊What is the definition of a function being continuous at a specific point?⍭ Generate me a similar question◊

Question

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

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To determine if $ \lim_{x o -1^+} h(x) $ and $ \lim_{x o -1^-} h(x) $ exist, we observe the graph. Both one-sided limits approach $ y = -5 $ as $ x $ approaches $ -1 $ from the right and left. Therefore, both limits exist. ‖ ‖ step 2 ⋮ To determine if $ \lim_{x o -1} h(x) $ exists, we check if the one-sided limits are equal. Since $ \lim_{x o -1^+} h(x) = -5 $ and $ \lim_{x o -1^-} h(x) = -5 $, the two-sided limit $ \lim_{x o -1} h(x) $ exists and is equal to $ -5 $. ‖ ‖ step 3 ⋮ To determine if $ h $ is defined at $ x = -1 $, we observe the graph. There is a hole at $ x = -1 $, indicating that $ h(-1) $ is not defined. ‖ ‖ step 4 ⋮ To determine if $ h $ is continuous at $ x = -1 $, we need $ h(-1) $ to be defined and $ \lim_{x o -1} h(x) = h(-1) $. Since $ h(-1) $ is not defined, $ h $ is not continuous at $ x = -1 $. ‖ ∻[question number] Answer∻ ***A*** ∻Key Concept∻ ⚹Existence of Limits⚹ ∻Explanation∻ ⚹For a limit to exist at a point, the left-hand limit and right-hand limit must both exist and be equal.⚹◊What is the definition of a function being continuous at a specific point?⍭ Generate me a similar question◊

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