Question

Describe how the graph of each function differs from the graph of f(x)=|x|. Then determine the domain and range.

A. g(x)= 0.6|x|



B. g(x)= 4|x−3|



C. g(x)= −|x+1|+5

Answer 1

A. We can compress the graph of the function
`f(x)=|x|` in the y-direction by multiplying the whole function by a constant C, such that
`0<C<1.` Since
`0<0.6<1,`, the graph of the function
`g(x)= 0.6|x|` is obtained from the graph of the function
`f(x)=|x|` by compression in the y-direction.

B. We can stretch the graph of the function
`f(x)=|x|` in the y-direction by multiplying the whole function by a constant C, such that
`C>1.` Since
`4>1,`, the graph of the function
`g(x)= 4|x-3|` is obtained from the graph of the function
`f(x)=|x|` by compression in the y-direction and translation 3 units to the right.

C. We can flip the graph of the function
`f(x)=|x|` upside down by multiplying the whole function by −1, then translate 1 unit to the left and 5 units up. Then we will get the function
`g(x)=-|x+1|+5.`