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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.

Write an equation for the given graph at the right. Use f(x) = ax - h + k as a model-example-1
User Uhu
by
8.0k points

1 Answer

1 vote

Answer:

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.

User Derhasi
by
8.2k points

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