Question

(a) graph the logarithmic function g(x)=\log_{2}(x + 2). to do this, plot two points on the graph of the function, and also draw the asymptote. then, click on the graph - a - function button. (b) give the domain and range of the function using interval notation. domain:

Explanation:

Step1: Determine the domain of logarithmic function

For the logarithmic function \( g(x)=\log_{2}(x + 2) \), the argument of the logarithm must be greater than 0. So we set up the inequality \( x+2>0 \).

Step2: Solve the inequality

Subtract 2 from both sides of the inequality \( x + 2>0 \), we get \( x>-2 \). In interval notation, the domain is \( (-2,\infty) \).

Answer:

The domain of the function \( g(x)=\log_{2}(x + 2) \) is \( (-2,\infty) \)