97.3k views
0 votes
What is the asymptote for the graph of this logarithmic function?

f(x) = log3(x – 1)

A.
x = -1
B.
x = 1
C.
y = -1
D.
y = 1
E.
y = 2

User Bumsik Kim
by
8.3k points

1 Answer

2 votes

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.

User Stefan Jarina
by
7.6k points