Question

give the equations of any vertical, horizontal, or oblique asymptotes for the graph of the rational function f(x) = (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 (type an equation.) b. there is no vertical asymptote.

Explanation:

Step1: Find vertical asymptote

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

Step2: Solve for x

Solving $x - 1=0$ gives $x = 1$.

Step3: Check degree for horizontal/oblique asymptote

The degree of the numerator and denominator is 1. Since the degrees are equal, the horizontal asymptote is $y=\frac{3}{1}=3$ (ratio of leading - coefficients), and there is no oblique asymptote (because degree of numerator = degree of denominator).

Answer:

A. The vertical asymptote is $x = 1$