Question

what is the equation of the vertical asymptote of ( f(x)=2log _{2}(x + 1)-3 )? enter your answer in the box. ( x=square )

Explanation:

Step1: Recall the domain of logarithmic functions

For a logarithmic function \(y = \log_b(u)\), the argument \(u>0\). In the function \(f(x)=2\log_2(x + 1)-3\), the argument \(u=x + 1\).

Step2: Set the argument equal to zero

We set \(x+1 = 0\) to find the vertical asymptote. Solving the equation \(x+1=0\) gives \(x=- 1\). As \(x\to - 1^{+}\), \(x + 1\to0^{+}\) and \(y = 2\log_2(x + 1)-3\to-\infty\).

Answer:

\(x=-1\)