Question
Where does the logarithmic function \(y=\log_4x\) have a vertical asymptote?(1 point)
Responses
\(x=0\)
x equals 0
\(x=4\)
x equals 4
The logarithmic function \(y=\log_4x\) has no vertical asymptote.
The logarithmic function y equals logarithm subscript 4 baseline x has no vertical asymptote.
\(y=4\)
Responses
\(x=0\)
x equals 0
\(x=4\)
x equals 4
The logarithmic function \(y=\log_4x\) has no vertical asymptote.
The logarithmic function y equals logarithm subscript 4 baseline x has no vertical asymptote.
\(y=4\)
Answers
GPT-4o mini
The logarithmic function \(y = \log_4 x\) has a vertical asymptote at \(x = 0\).
In general, logarithmic functions have a vertical asymptote at the value of \(x\) at which the function is undefined, which occurs when the argument of the logarithm is zero or negative. Since \(y = \log_4 x\) is defined for \(x > 0\), it approaches negative infinity as \(x\) approaches 0 from the right.
So the correct response is:
\(x = 0\)
In general, logarithmic functions have a vertical asymptote at the value of \(x\) at which the function is undefined, which occurs when the argument of the logarithm is zero or negative. Since \(y = \log_4 x\) is defined for \(x > 0\), it approaches negative infinity as \(x\) approaches 0 from the right.
So the correct response is:
\(x = 0\)