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

Question

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

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To determine which limit expressions agree with the graph, we first analyze the graph of the function $h$. ‖ ‖ step 2 ⋮ The graph shows that as $x$ approaches $-4$ from either direction, $h(x)$ approaches $-2$. Therefore, $ \lim_{x ightarrow -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 ightarrow 0^+} h(x) eq 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 ightarrow 4^-} h(x) eq 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.⚹◊What is the limit expression for $h(x)$ as $x$ approaches $4$ from the left in the given graph?⍭ Generate me a similar question◊

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