Question

find all asymptotes, x - intercepts, and y - intercepts for the graph of the rational function and sketch the graph of the function.
f(x) = \frac{5x}{x^{2}-8x + 16}
find all vertical asymptotes. select the correct choice below and, if necessary, fill in the answer box within your choice.
a. x=
(simplify your answer. use a comma to separate answers as needed.)
b. there are no vertical asymptotes.

Explanation:

Step1: Set denominator equal to 0

Set $x^{2}-8x + 16=0$.

Step2: Factor the quadratic

Factor $x^{2}-8x + 16$ to $(x - 4)^{2}=0$.

Step3: Solve for x

Solving $(x - 4)^{2}=0$ gives $x=4$.

Answer:

A. $x = 4$