Question

1. a graph of the function ( y=log _{2}(x + 4) ) is shown below.

4a state the equation of the vertical asymptote of ( y=log _{2}(x + 4) ).

Explanation:

Step1: Determine the domain of the logarithmic function

For the function \(y = \log_{2}(x + 4)\), the argument of the logarithm must be positive. So we set \(x+4>0\).

Step2: Solve the inequality for \(x\)

Subtract \(4\) from both sides of the inequality \(x + 4>0\). We get \(x>- 4\).

Step3: Identify the vertical asymptote

The vertical asymptote occurs at the value of \(x\) that makes the argument of the logarithm equal to \(0\). Since \(x+4 = 0\) when \(x=-4\), the vertical asymptote is \(x=-4\).

Answer:

\(x = - 4\)