Questions: What is the equation of the vertical asymptote for the graph of the rational function g(x)=6/(x-1)? x=1 x=-1 x=6 x=1/6

Transcript text: What is the equation of the vertical asymptote for the graph of the rational function $g(x)=\frac{6}{x-1}$ ? $x=1$ $x=-1$ $x=6$ $x=\frac{1}{6}$

Solution

Solution Steps

To find the vertical asymptote of a rational function, we need to determine the values of $ x $ that make the denominator equal to zero, as these are the points where the function is undefined. For the function $ g(x) = \frac{6}{x-1} $, set the denominator $ x-1 $ equal to zero and solve for $ x $.

Step 1: Identify the Function

We are given the rational function $ g(x) = \frac{6}{x-1} $.

Step 2: Set the Denominator to Zero

To find the vertical asymptote, we need to determine where the function is undefined. This occurs when the denominator is equal to zero: \[ x - 1 = 0 \]

Step 3: Solve for $ x $

Solving the equation $ x - 1 = 0 $ gives: \[ x = 1 \]