Question

How do you write `f(x) = 4 |x-3|` as piecewise functions?

Answer 1

`f(x)={(4x-12color(white)("xxx") if x>= 3),(12-4xcolor(white)("xxx")if x < 3):}`

Explanation:

If `x >= 3` then `abs(x-3)=x-3`
`color(white)("XXX")rArr 4abs(x-3)=4(x-3)=4x-12`

If `x < 3` then `abs(x-3) = -(x-3)=3-x`
`color(white)("XXX")rArr 4abs(x-3)=4(3-x)=12-4x`