# Week 12 – Precalc 11

This week in precalc 11 we learned about absolute value functions.
An absolute value function is a function that has an algebraic expression within absolute value symbols in it.
*(the absolute value of a number is its distance from zero on a number line)*
The absolute value parent function is written as f (x) = | x | which is also defined as

f (x) = {x if x >0
0 if x = 0
-x if x < 0

We also learned how to solve equations with absolute values in it. There are some simple steps do to so. First, you isolate the absolute value expression, then you put the quantity inside the absolute notation equal to + and – the quantity on the other side of the equation
You then solve for the variable in both equations, and always remember to always check the answers to make sure you got the right answer and not an extraneous solution.
Here’s an example:
|2x-1| = 5
We write the equations with the different signs + and – and solve them.
|2x-1| = 5 and |2x-1| = – 5

1.) |2x-1| = 5
2x – 1 = 5
2x = 6
x = 3

2.) |2x-1| = – 5
2x – 1 = – 5
2x = – 4
x = – 2

The answers are 3 and – 2. To make sure we got the right answer, we check by substituting these answers into the original equation.