Question

find the domain and vertical asymptote of ( f(x)=ln (x - 3) ). enter the domain in interval notation. domain: help (intervals) vertical asymptote help (numbers) note: you can earn partial credit on this problem. preview my answers submit answers show me another you have attempted this problem 0 times. you have 5 attempts left before new version will be requested. you have unlimited attempts remaining. email instructor

Explanation:

Step1: Find the domain

The domain of \(y = \ln(u)\) is \(u>0\). For \(f(x)=\ln(x - 3)\), set \(x-3>0\).
\(x-3>0\Rightarrow x>3\)
In interval notation, the domain is \((3,\infty)\)

Step2: Find the vertical asymptote

The vertical asymptote of \(y = \ln(u)\) occurs at \(u = 0\). For \(f(x)=\ln(x - 3)\), set \(x-3=0\)
\(x-3=0\Rightarrow x = 3\)

Answer:

Domain: \((3,\infty)\)
Vertical asymptote: \(x = 3\)