This is the graph of function $f$. Dashed lines represent asymptotes.

Select the $x$-values at which $f$ has a removable discontinuity.

Choose all answers that apply:
A) $x=-5$
B $x=1$
ㄱ $x=5$

D None of the above

Question

This is the graph of function $f$. Dashed lines represent asymptotes.

Select the $x$-values at which $f$ has a removable discontinuity.

Choose all answers that apply:
A) $x=-5$
B $x=1$
ㄱ $x=5$

D None of the above

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the points on the graph where there is a removable discontinuity. A removable discontinuity occurs where a function is not defined at a point, but the limit exists. ‖ ‖ step 2 ⋮ From the graph, observe that at $x = -5$, there is an open circle, indicating a removable discontinuity. ‖ ‖ step 3 ⋮ At $x = 1$ and $x = 5$, there are vertical dashed lines, indicating vertical asymptotes, not removable discontinuities. ‖ ‖ step 4 ⋮ Therefore, the only removable discontinuity is at $x = -5$. ‖ ***A*** ∻Key Concept∻ ⚹Removable Discontinuity⚹ ∻Explanation∻ ⚹A removable discontinuity occurs at a point where a function is not defined, but the limit exists. In this case, the open circle at $x = -5$ indicates such a discontinuity.⚹◊What is the equation of the function $f$ given the graph description provided by the user?⍭ Generate me a similar question◊

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