Question

Write an equation for the

given graph at the right. Use f(x) = ax - h + k as a model. Then give me the
vertex, domain and range.

Answer 1

See below

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.