2.7

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2.7

  1. 1. 2.7 ABSOLUTE VALUEFUNCTIONS AND GRAPHS
  2. 2. ABSOLUTE VALUE FUNCTION The simplest form (parent graph) of an absolute value function is f ( x ) = x
  3. 3. ABSOLUTE VALUE FUNCTION The graph of f ( x ) = x is V-shaped and symmetric about a vertical line called the axis of symmetry.  The graph also has a single maxima point or minima point, called a vertex
  4. 4. EXAMPLEMake a table of values, then graph the function. Describethe transformation from the parent function.y = x −4
  5. 5. EXAMPLEMake a table of values, then graph the function. Describethe transformation from the parent function.f ( x) = x + 2 + 3
  6. 6. EXAMPLEGraph the equation. Describe the transformation from theparent function. 1y= x 2
  7. 7. EXAMPLEGraph the equation. Describe the transformation from theparent function.
  8. 8. TRANSFORMATIONS OF THEABSOLUTE VALUE FUNCTION
  9. 9. GENERAL FORM OF THEABSOLUTE VALUE FUNCTIONWhen translations, stretches andcompressions are combined for AbsoluteValue Functions, we derive the general form:y =a x−h +kThe stretch or compression factor is |a|, thevertex is located at (h, k), and the axis ofsymmetry is the line x = h
  10. 10. EXAMPLEWithout graphing, what are the vertex and axis ofsymmetry of the graph of:y =3 x−2 +4
  11. 11. EXAMPLEWithout graphing, what are the vertex and axis ofsymmetry of the graph of:y = −2 x − 1 − 3
  12. 12. EXAMPLEWithout graphing, what are the vertex and axis ofsymmetry of the graph of:
  13. 13. WRITING AN ABSOLUTEVALUE FUNCTION FROM AGRAPH1. Identify the vertex2. Identify a, by finding the slope of the branch on the right3. Write the equation
  14. 14. EXAMPLEWhat is the equation of the absolute valuefunction?
  15. 15. EXAMPLEWhat is the equation of the absolute valuefunction?
  16. 16. WITHOUT USING A TABLE OFVALUES GRAPH THE FUNCTION
  17. 17. HOMEWORK Page 111  #9 – 21 odd  #23 – 30 all

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