Given that the function f(x)=1/x is replaced by g(x)=1/x+23 , find the equation of the horizontal asymptote of the new graph.(1 point) y=

Answer 1

To find the horizontal asymptote of the function \( g(x) = \frac{1}{x} + 23 \), we need to analyze the behavior of the function as \( x \) approaches infinity (or negative infinity).

1. As \( x \to \infty \): \[ g(x) = \frac{1}{x} + 23 \to 0 + 23 = 23 \]

2. As \( x \to -\infty \): \[ g(x) = \frac{1}{x} + 23 \to 0 + 23 = 23 \]

In both cases, the function approaches the value 23. Therefore, the horizontal asymptote of the graph of \( g(x) \) is:

\[ y = 23 \]

So the equation of the horizontal asymptote is \( \boxed{23} \).