Question

select the correct answer. what is the equation of the asymptote for this function? f(x) = ln x + 5 a. x = 0 b. x = -5 c. y = 0 d. y = -5

Explanation:

Step1: Recall parent function asymptote

The parent function $g(x)=\ln x$ has a vertical asymptote at $x=0$, since $\ln x$ is undefined for $x\leq0$.

Step2: Analyze vertical shift effect

The function $f(x)=\ln x + 5$ is a vertical shift of $g(x)$ (shifted up 5 units). Vertical shifts do not change the vertical asymptote of a logarithmic function.

Answer:

A. $x = 0$