Question

How do you write `f(x)= |-18x-17|` as a piecewise function?

Answer 1

Please see below.

Explanation:

We can write `abs(u) = {(u,"if",u >= 0),(-u,"if",u < 0):}`

So,

`abs(-18x-17) = {(-18x-17,"if",-18x-17 >= 0),(-(-18x-17),"if",-18x-17 < 0):}`

`= {(-18x-17,"if",-18x-17 >= 0),(18x+17,"if",-18x - 17 < 0):}`

`= {(-18x-17,"if",-18x >= 17),(18x+17,"if",-18x < 17):}`

`= {(-18x-17,"if",x <= -17/18),(18x+17,"if",x > -17/18):}`