Question

How do you find the domain and range of `y=4absx`?

Answer 1

`x inRR`
`y in[0,+oo)`

Explanation:

`"making a 'quick' sketch of the function will help"`

`"choose values of x and calculate y"`

`color(red)(x=0)toy=4|0|=0to(0,0)`

`color(red)(x=1)toy=4|1|=4to(1,4)`

`color(red)(x=2)toy=4|2|=8to(2,8)`

`color(red)(x=-1)toy=4|-1|=4to(-1,4)`

`color(red)(x=-2)toy=4|-2|to(-2,8)`

`"plotting these points gives"`
graph{4|x| [-11.25, 11.24, -5.62, 5.635]}

`"from the graph we can see domain/range"`

`"domain is " x inRR`

`"range is " [0,+oo)`