Consider the graph of function $g$. The dashed lines represent asymptotes.

Which limit expressions agree with the graph?

Choose all answers that apply:
A) $\lim _{x \rightarrow 3} g(x)=\infty$

В $\lim _{x \rightarrow 3^{-}} g(x)=\infty$
(c) $\lim _{x \rightarrow 3^{+}} g(x)=\infty$

Question

Consider the graph of function $g$. The dashed lines represent asymptotes.

Which limit expressions agree with the graph?

Choose all answers that apply:
A) $\lim _{x \rightarrow 3} g(x)=\infty$

В $\lim _{x \rightarrow 3^{-}} g(x)=\infty$
(c) $\lim _{x \rightarrow 3^{+}} g(x)=\infty$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ We need to determine which limit expressions agree with the graph of the function $g$. The graph shows that as $x$ approaches $3$, the function $g(x)$ approaches infinity from both the left and the right. ‖ ‖ step 2 ⋮ The limit expression $A$ is $ \lim _{x \rightarrow 3} g(x)=\infty$. This means that as $x$ approaches $3$ from either direction, $g(x)$ approaches infinity. This is consistent with the graph. ‖ ‖ step 3 ⋮ The limit expression $B$ is $ \lim _{x \rightarrow 3^{-}} g(x)=\infty$. This means that as $x$ approaches $3$ from the left, $g(x)$ approaches infinity. This is consistent with the graph. ‖ ‖ step 4 ⋮ The limit expression $C$ is $ \lim _{x \rightarrow 3^{+}} g(x)=\infty$. This means that as $x$ approaches $3$ from the right, $g(x)$ approaches infinity. This is consistent with the graph. ‖ ∻Answer∻ ⚹ A, B, C ⚹ ∻Key Concept∻ ⚹Limit expressions and asymptotes⚹ ∻Explanation∻ ⚹The graph shows that as $x$ approaches $3$ from both the left and the right, $g(x)$ approaches infinity, which means all the given limit expressions are correct.⚹◊What is the relationship between the graph of a function and its limit expressions as x approaches a specific value⍭ Generate me a similar question◊

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