Here we need to see which statement describes the vertical asymptotes of the given function.
The correct option is the first one, the function does not have any vertical asymptote.
We define asymptotes as tendencies that never reach a given value.
Particularly, vertical asymptotes usually happen when a denominator becomes zero.
In this case, we have the function:
[tex]f(x) = \frac{x^2 - 64}{8x - 64}[/tex]
The denominator becomes zero when:
8*x = 64
x = 64/8 = 8
But notice that the numerator also becomes zero at this point. We can rewrite the numerator as:
[tex]x^2 - 64 = (x + 8)*(x - 8)[/tex]
Then the function can be written as:
[tex]f(x) = \frac{(x - 8)*(x + 8)}{8*x - 64} = \frac{(x - 8)*(x + 8)}{8*(x - 8)} = \frac{(x + 8)}{8}[/tex]
Notice that now the denominator can't become zero, this means that the function does not have any vertical asymptote.
Then the correct option is the first one.
If you want to learn more, you can read:
https://brainly.com/question/4084552
