Answer:
See below
Step-by-step explanation:
For the model function [tex]f(x)=a|x-h|+k[/tex], [tex](h,k)[/tex] is the vertex, and [tex]a[/tex] is the horizontal growth or shrink factor.
We know that our vertex is [tex](-1.5,0)[/tex] from our graph, so we'll need to determine the value of [tex]a[/tex] by using one of the points on the graph:
[tex]f(x)=a|x-h|+k\\\\f(x)=a|x-(-1.5)|+0\\\\f(x)=a|x+1.5|\\\\f(0)=a|0+1.5|\\\\3=a|1.5|\\\\3=1.5a\\\\2=a[/tex]
Thus, our equation for the given graph is [tex]f(x)=2|x+1.5|[/tex].
The domain of a function is the set of all existing real x-values, thus, our domain for the given function is [tex](-\infty,\infty)[/tex], or all real x-values.
The range of a function is the set of all existing real y-values, thus, our range for the given function is [tex][-1,\infty)[/tex], or all real y-values starting with y=-1 which is included.
