Question

find the equation of the vertical asymptote $f(x)=\log(x + 2)$

Explanation:

Step1: Recall the domain of logarithmic function

The domain of \(y = \log(u)\) is \(u>0\). For \(y=\log(x + 2)\), we set \(x+2>0\).

Step2: Solve the inequality for \(x\)

Subtract \(2\) from both sides of \(x + 2>0\). We get \(x>- 2\). As \(x\) approaches \(-2\) from the right (\(x\to - 2^{+}\)), the function \(y = \log(x + 2)\) has a vertical asymptote.

Answer:

\(x=-2\)