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