Question

How do you write `p(x) = |x-1| +4` as a piecewise function?

Answer 1

`p(x)=-x+5 :x in (-oo,1)`
`p(x) = +x+3: x in [1, +oo)`

Explanation:

`p(x) =abs(x-1)+4`

`p(x) =-(x-1)+4 =-x+5`
where `x-1<0 -> x in (-oo, +1)`

`p(x) =+(x-1)+4 = +x+3`
where `x-1>=0 -> x in [1, +oo)`

This can be more easily visualised from the graph pf `p(x)` below.

graph{abs(x-1)+4 [-9.96, 10.04, -0.64, 9.36]}