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 answer

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 positive or negative infinity.

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

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

In both cases, the function approaches 23. Therefore, the horizontal asymptote of the function \( g(x) = \frac{1}{x} + 23 \) is:

\[ y = 23 \]

Thus, the equation of the horizontal asymptote is \( \boxed{y = 23} \).