Question

use the graph shown to find the following.
(a) the domain and range of the function
(b) the intercepts, if any
(c) horizontal asymptotes, if any
(d) vertical asymptotes, if any
(e) oblique asymptotes, if any
(a) the domain of the function is
(type your answer in interval notation. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Analyze the domain

The domain of a function is the set of all possible \(x -\)values. Looking at the graph, there are vertical dashed lines (which represent vertical asymptotes) at \(x = - 2\) and \(x=2\). The function is not defined at \(x=-2\) and \(x = 2\). So, we use interval notation. The domain is all real numbers except \(x=-2\) and \(x = 2\). In interval notation, this is \((-\infty,-2)\cup(-2,2)\cup(2,\infty)\)

Answer:

\((-\infty,-2)\cup(-2,2)\cup(2,\infty)\)