Question

which statement describes the vertical asymptotes of the graph of f(x) = (x^2 - 64)/(8x - 64)? the graph has no vertical asymptote. the graph has vertical asymptotes at both x = 8 and x = -8. the graph has a vertical asymptote at x = -8 only. the graph has a vertical asymptote at x = 8 only.

Explanation:

Step1: Recall vertical - asymptote condition

Vertical asymptotes of a rational function $y = \frac{f(x)}{g(x)}$ occur at the values of $x$ for which $g(x)=0$ and $f(x)
eq0$. Given $y=\frac{x^{2}-64}{8x - 64}=\frac{(x + 8)(x - 8)}{8(x - 8)}$.

Step2: Simplify the function

Cancel out the common factor $(x - 8)$ (for $x
eq8$), we get $y=\frac{x + 8}{8},x
eq8$. The only value that makes the original denominator zero and is not canceled out is $x = 8$.

Answer:

The graph has a vertical asymptote at $x = 8$ only.