Identifying Removable Discontinuities

Question

Which of the following is an example of a function with a removable discontinuity? Remember that a removable discontinuity occurs when the function is undefined at a point even though the limit exists there, and the discontinuity can be "removed" by redefining the function at that point.

Accepted Answer

The function $$f(x)=\begin{cases} \frac{(x-2)*(x+3)}{x-2} & x
eq 2 \ 5 & x=2 \end{cases}$$, which simplifies to $$x+3$$ for all x except at $$x=2$$ and can be redefined to be continuous.

Answer

The function $$k(x)=\frac{(x-2)*(x+3)}{(x-2)^2}$$, where cancellation is incomplete and the discontinuity at $$x=2$$ remains essential.

Answer

The function $$h(x)=|x-2|$$, which is continuous everywhere but not differentiable at $$x=2$$ due to a sharp corner.

Answer

The function $$g(x)=\frac{x+1}{x-2}$$, which has a vertical asymptote at $$x=2$$ and cannot be redefined to remove the discontinuity.

Rank	User	Correct Count	Attempt Count	Total Time	Score
#1	bhavyarajdharnia	1	1	0m 00s	100
#2	sophiejcg07	0	1	0m 00s	-10
#3	lesleiman	1	1	2m 17s	-37
#4	jonathanchoi1976	0	1	0m 58s	-68

Identifying Removable Discontinuities

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