Question

Math

Posted 3 months ago

```
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
```

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Answer from Sia

Posted 3 months ago

Solution by Steps

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.

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