Question

How do you write `y = |x+5|` as a piecewise function?

Answer 1

`|x+5|=x+5` if `x>=-5` and

`|x+5|=-x-5` if `x<-5`

Explanation:

`|a|` is a split function as

`|a|=a` if `a>=0` and `|a|=-a` if `a<0`

Similarly, we can write `y=|x+5|` as

`|x+5|=x+5` if `x+5>=0` i.e. `x>=-5` and

`|x+5|=-x-5` if `x+5<0` i.e. `x<-5`