Question

Write an equation for the

Answer 1

Answer:

See below

Step-by-step explanation:

For the model function $f(x)=a|x-h|+k$, $(h,k)$ is the vertex, and $a$ is the horizontal growth or shrink factor.

We know that our vertex is $(-1.5,0)$ from our graph, so we'll need to determine the value of $a$ by using one of the points on the graph:

$f(x)=a|x-h|+k\\\\f(x)=a|x-(-1.5)|+0\\\\f(x)=a|x+1.5|\\\\f(0)=a|0+1.5|\\\\3=a|1.5|\\\\3=1.5a\\\\2=a$

Thus, our equation for the given graph is $f(x)=2|x+1.5|$.

The domain of a function is the set of all existing real x-values, thus, our domain for the given function is $(-\infty,\infty)$, 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 $[-1,\infty)$, or all real y-values starting with y=-1 which is included.