Step-by-step explanation:
The asymptote for the graph of the logarithmic function f(x) = log3(x – 1) is x = 1. As x approaches 1, the value of f(x) approaches negative infinity.
Related topics:
Exponential functions
Logarithmic equations
Graphing logarithmic functions
An asymptote is a line that a graph approaches but never touches or crosses. In the case of logarithmic functions, there can be vertical asymptotes and horizontal asymptotes.
For the given logarithmic function f(x) = log3(x – 1), we are looking for the vertical asymptote.
To find the vertical asymptote, we need to consider the domain of the function. In this case, the domain is all values of x greater than 1, since we have (x - 1) inside the logarithm and the logarithm is not defined for negative or zero values.
As x approaches 1 from the right side (values greater than 1), the function approaches negative infinity. Therefore, the vertical asymptote for the graph of f(x) = log3(x – 1) is x = 1.
So, the correct answer is B. x = 1.
I hope this helps! Let me know if you have any further questions.