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

1 Answer
Jun 24, 2017

Answer:

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):}#