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 $x=-5$
В $\quad x=1$
С $x=5$

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 $x=-5$
В $\quad x=1$
С $x=5$

D None of the above

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the points where the function $f$ has discontinuities. From the graph, we see vertical asymptotes at $x = 1$ and $x = 5$. ‖ ‖ step 2 ⋮ Determine if these discontinuities are removable. A removable discontinuity occurs if the limit exists at that point but the function is not defined or does not match the limit. ‖ ‖ step 3 ⋮ Check $x = -5$. There is a filled circle at $(-5, -4)$, indicating that the function is defined at this point. However, there is no indication of a discontinuity at $x = -5$. ‖ ‖ step 4 ⋮ Check $x = 1$ and $x = 5$. Both points have vertical asymptotes, which are non-removable discontinuities. ‖ ‖ step 5 ⋮ Conclude that there are no removable discontinuities in the given options. ‖ ***D*** ∻Key Concept∻ ⚹Removable Discontinuity⚹ ∻Explanation∻ ⚹A removable discontinuity occurs when a function has a hole at a point, but the limit exists. In this case, there are no such points.◊What is the definition of a removable discontinuity in a function?⍭ Generate me a similar question◊⚹

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