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Absolute value functions

Absolute value functions. Absolute value. =-(-3) If c is a real number, then is the distance from c to 0 on the number line The distance from the origin. For example, =8 can be read as the distance from x to 4 is 8 units. properties. c =3; . solving. Solved by using the definitions

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Absolute value functions

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  1. Absolute value functions

  2. Absolute value • =-(-3) • If c is a real number, then is the distance from c to 0 on the number line • The distance from the origin

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

  4. properties • c=3;

  5. solving • Solved by using the definitions • Graphing 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!

  6. Fake solutions • 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!

  7. EXAMPLE • Think back to the first example: • We said this read as, the distance from x to 4 is 8 units • Two choices for an answer • One is positive, one is negative • When you solve, you take both into account

  8. Solve it!

  9. Now check 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!

  10. Solve, and check by graphing!

  11. Summary • Each absolute value equation can be though of as an x value a certain distance from a certain point • Therefore, there is typically more than one answer • Sometimes there are fake answers • Check in calculator • Plug in left side of equation for y1 • Plug in right side of equation for y2 • Look for intersection points • These must match your answers • If they do not, the root is extraneous

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