Gr10 piecewise functions

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Gr10 piecewise functions

  1. 1. Algebra II Piecewise Functions Edited by Mrs. Harlow
  2. 2. 2-6: Special Functions <ul><li>Constant </li></ul><ul><li>Identity </li></ul><ul><li>Absolute Value </li></ul><ul><li>Step/Greatest Integer </li></ul><ul><li>Piecewise </li></ul>
  3. 3. Constant Function: A linear function in the form y = b. y = 3
  4. 4. Identity Function: A linear function in the form y = x. y=x
  5. 5. <ul><li>Up to now, we’ve been looking at functions represented by a single equation. </li></ul><ul><li>In real life, however, functions are represented by a combination of equations, each corresponding to a part of the domain. </li></ul><ul><li>These are called piecewise functions. </li></ul>
  6. 6. <ul><li>One equation gives the value of f (x) when x ≤ 1 </li></ul><ul><li>And the other when x>1 </li></ul>
  7. 7. Evaluate f(x) when x=0, x=2, x=4 <ul><li>First you have to figure out which equation to use </li></ul><ul><li>You NEVER use both </li></ul>X=0 This one fits into the top equation So: 0+2=2 f(0)=2 X=2 This one fits here So: 2(2) + 1 = 5 f(2) = 5 X=4 This one fits here So: 2(4) + 1 = 9 f(4) = 9
  8. 8. Graph: <ul><li>For all x’s < 1, use the top graph (to the left of 1) </li></ul><ul><li>For all x’s ≥ 1, use the bottom graph (to the right of 1) </li></ul>
  9. 9. x=1 is the breaking point of the graph. To the left is the top equation. To the right is the bottom equation.
  10. 10. Graph:
  11. 11. Greatest Integer Function: A function in the form y = [ x ] <ul><li>Note: [ x ] means the greatest integer less than or equal to x . For example, the largest integer less than or equal to -3.5 is -4. </li></ul>2 4 6 – 2 – 4 – 6 x 2 4 6 – 2 – 4 – 6 y y =[ x ]
  12. 12. Greatest Integer Function: A function inthe form y = [ x ] <ul><li>Graph y = [ x ] + 2 by completing the t-table: </li></ul>x y -3 - 2.75 -2.5 -2.25 -2 -1.75 -1.5 -1.25 -1 0 1 2 4 6 – 2 – 4 – 6 x 2 4 6 – 2 – 4 – 6 y x y -3 y = [-3]+2=-1 - 2.75 y = [-2.75]+2=-1 -2.5 y = [-2.5]+2=-1 -2.25 y = [-2.25]+2=-1 -2 y = [-2]+2 =0 -1.75 y = [-1.75]+2=0 -1.5 y = [-1.5]+2=0 -1.25 y = [-1.25]+2=0 -1 y = [-1]+2=1 0 y = [0]+2=2 1 y = [1]+2=3
  13. 13. Step Functions
  14. 15. Graph :
  15. 17. <ul><li>Labor costs at the Fix-It Auto Repair Shop are $60 per hour or any fraction thereof. Draw a graph that represents this situation. </li></ul>
  16. 18. Assignment

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