ABSOLUTE VALUE FUNCTIONS

=-(-3)If c is a real number, then is the distance

from c to 0 on the number lineThe distance from the origin

ABSOLUTE VALUE

For example, =8 can be read as the distance from x to 4 is 8 units

• c=3;

PROPERTIES

Solved by using the definitionsGraphing techniques are also an important

part!

GO JAGUARS!!!There are two answers to most absolute value equations. You must solve for the positive case and the negative case…but

math student be aware…

THERE ARE FAKE SOLUTIONS!

SOLVING

• Commonly called extraneous solutions• What is an extraneous solution?• Some solutions do not make the original

equation true when checked by substitution

• What to do?• CHECK ALL SOLUTIONS BY

SUBSITUTING BACK IN, OR BY GRAPHING!

FAKE SOLUTIONS

Think back to the first example:

We said this read as, the distance from x to 4 is 8 units

Two choices for an answerOne is positive, one is negative

When you solve, you take both into account

EXAMPLE

SOLVE IT!

• Put in Calculator as 2 equations• Look at the points on the graph where

the lines intersect. The x values of the intersection must match your answer or it is an extraneous root!

• Go to Calculator!• OH yeah….GO JAGUARS!

NOW CHECK IT!

Solve, and check by graphing!

|𝒙+𝟒|=𝟓𝒙 −𝟐

Each absolute value equation can be though of as an x value a certain distance

from a certain pointTherefore, there is typically more than one

answerSometimes there are fake answers

Check in calculator1. Plug in left side of equation for y1

2. Plug in right side of equation for y23. Look for intersection points

4. These must match your answers5. If they do not, the root is extraneous

SUMMARY