Question

give the equations of any vertical, horizontal, or oblique asymptotes for the graph of the rational function $f(x)=\frac{3x + 2}{x - 1}$. select the correct answer below and, if necessary, fill in the answer box to complete your choice. a. the vertical asymptote is $x = 1$. (type an equation.) b. there is no vertical asymptote. select the correct answer below and, if necessary, fill in the answer box to complete your choice. a. the horizontal asymptote is. (type an equation.) b. there is no horizontal asymptote.

Explanation:

Step1: Find vertical asymptote

Set denominator equal to 0. For $f(x)=\frac{3x + 2}{x - 1}$, we solve $x-1=0$, so $x = 1$ is the vertical asymptote.

Step2: Find horizontal asymptote

Since the degree of the numerator and denominator are the same (both degree 1), the horizontal asymptote is $y=\frac{\text{leading - coefficient of numerator}}{\text{leading - coefficient of denominator}}$. The leading - coefficient of the numerator is 3 and of the denominator is 1. So $y = 3$.

Answer:

A. The vertical asymptote is $x = 1$.
A. The horizontal asymptote is $y=3$.