Home > Algebra > Graphs of Absolute Value Equations

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

Answer 1

Nathan Axel

See explanation.

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

The definition says that:

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):}#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Hazel Anglin

f(x) = \begin{cases} x+9, & \text{if } x+9 \geq 0 \ -(x+9), & \text{if } x+9 < 0 \end{cases}

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.