We want to see if all rational functions always have at least one asymptote or hole.
The answer is C:
" Yes, the function will have either a vertical asymptote or hole for any values that cause the denominator to be equal to zero"
A rational function is something like:
[tex]f(x) = \frac{q(x)}{p(x)}[/tex]
Where q(x) and p(x) are polynomials.
The asymptotes or holes happen when the denominator is equal to zero and the numerator don't.
Now, in the cases where the numerator and denominator become zero for the same value of x, it means that we can factorize the polynomials and remove the common factor. So there we do not have a hole nor asymptote.
Now, because the denominator becomes equal to zero, this means that we are dividing by a reallly small value, then the quotient will tend to infinity or negative infinity, this means that we will have a vertical asymptote.
Then the correct option is C:
Yes, the function will have either a vertical asymptote or hole for any values that cause the denominator to be equal to zero
If you want to learn more, you can read:
https://brainly.com/question/4084552
