which statement describes the vertical asymptotes of the graph of $f(x)=\frac{x^{2}-64}{8x - 64}$?\nthe…

Explanation:

Step1: Recall vertical - asymptote condition

Vertical asymptotes occur where the denominator of a rational function is zero and the numerator is non - zero. Set the denominator equal to zero: $8x - 64=0$.

Step2: Solve the denominator equation

Solve $8x - 64 = 0$ for $x$. Add 64 to both sides: $8x=64$. Then divide both sides by 8, we get $x = 8$.

Step3: Check the numerator at $x = 8$

Substitute $x = 8$ into the numerator $x^{2}-64$. When $x = 8$, $x^{2}-64=8^{2}-64=64 - 64=0$.

Step4: Factor the numerator and denominator

Factor the numerator $x^{2}-64=(x + 8)(x - 8)$ and the denominator $8x-64 = 8(x - 8)$. Then $f(x)=\frac{(x + 8)(x - 8)}{8(x - 8)}=\frac{x + 8}{8},x\neq8$.

Answer:

The graph has no vertical asymptote.