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)=x−16, 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)=x−16.
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
Final Answer
The vertical asymptote of the function is \\(\boxed{x = 1}\\).