determine the domain and the range of the piece - wise function shown to the right. then write an equation…

Explanation:

Step1: Identify domain from graph

The graph extends infinitely to the left and right along the x - axis. So, the domain includes all real numbers.

Step2: Identify range from graph

The graph has two horizontal parts. The upper part is at (y = 4) (open - circle) and the lower part is at (y=- 4) (open - circle). The range is all real numbers except (y = 4) and (y=-4).

Step3: Write piece - wise function

For (x < - 3), (y = 4) (open - circle, so not included: (y = 4,x<-3)). For (x\geq - 3), (y=-4) (open - circle, so not included: (y=-4,x\geq - 3)). The piece - wise function is (f(x)=\begin{cases}4, & x < - 3\-4, & x\geq - 3\end{cases})

Answer:

Domain: ((-\infty,\infty)) Range: ((-\infty,-4)\cup(-4,4)\cup(4,\infty)) Function: (f(x)=\begin{cases}4, & x < - 3\-4, & x\geq - 3\end{cases})