Question
When the function f(x)=1x
is replaced by the function g(x)=1x−22
, what is the equation of the horizontal asymptote of the graph of g(x)
?(1 point)
Responses
y=−22
y equals negative 22
x=−22
x equals negative 22
x=22
x equals 22
y=22
is replaced by the function g(x)=1x−22
, what is the equation of the horizontal asymptote of the graph of g(x)
?(1 point)
Responses
y=−22
y equals negative 22
x=−22
x equals negative 22
x=22
x equals 22
y=22
Answers
GPT-4o mini
To find the horizontal asymptote of the function \( g(x) = \frac{1}{x - 22} \), we look at the behavior of \( g(x) \) as \( x \) approaches positive or negative infinity.
1. As \( x \to \infty \):
\[ g(x) = \frac{1}{x - 22} \to \frac{1}{\infty} = 0. \]
2. As \( x \to -\infty \):
\[ g(x) = \frac{1}{x - 22} \to \frac{1}{-\infty} = 0. \]
In both cases, the function approaches \( 0 \). Therefore, the horizontal asymptote of the function \( g(x) \) is:
\[
y = 0.
\]
Since this option is not given in your responses, it appears there was a misunderstanding in the options provided. The correct answer should be \( y = 0 \), but among the given options, none reflect this accurately.
If analyzing the options strictly in the format indicated, be aware that no other choice is accurate given the correct properties of horizontal asymptotes for this function.
1. As \( x \to \infty \):
\[ g(x) = \frac{1}{x - 22} \to \frac{1}{\infty} = 0. \]
2. As \( x \to -\infty \):
\[ g(x) = \frac{1}{x - 22} \to \frac{1}{-\infty} = 0. \]
In both cases, the function approaches \( 0 \). Therefore, the horizontal asymptote of the function \( g(x) \) is:
\[
y = 0.
\]
Since this option is not given in your responses, it appears there was a misunderstanding in the options provided. The correct answer should be \( y = 0 \), but among the given options, none reflect this accurately.
If analyzing the options strictly in the format indicated, be aware that no other choice is accurate given the correct properties of horizontal asymptotes for this function.