Question

Write the absolute value function y43 - 2 + 11 as a piecewise function.

Answer 1

We have the following function given:

`y=4\left|x-2\right|+11`

By definition we have:

`\left|x\right|=x,x\ge0`
`\left|x\right|=-x,x<0`

And we want to rewrite the expression in a piecewise function so we can do this:

`y=4(x-2)+11=4x+3`
`y=4(-x+2)+11=-4x+19`

And the solution would be:

`y=-4x+19,x<2`

`y=4x+3,x\ge2`