Question

How do you write `f(x)= |x+9|` as a piecewise function?

Answer 1

See explanation.

Explanation:

To write this function as a piecewise function you have to use the definition of absolute value.

The definition says that:

`|x|={(x, x>=0),(-x, x<0) :}`

Applying this definition to your function you get:

`|x+9|={(x+9,x+9>=0),(-x-9,x+9<0):}`

After simplifying the inequalities you get:

`|x+9|={(x+9,x>=-9),(-x-9,x<-9):}`

So finally you can write the function as:

`f(x)={(x+9,x>=-9),(-x-9,x<-9):}`