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Lecture 3.2 bt

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Lecture 3.2 bt

  1. 1. Today’s Agenda  Attendance / Announcements ◦ Need TI Graphing Calculator ◦ Exam 2 – Friday 10/11  Covers Chapters 3.1 to 3.7  Questions?  Sections 3.2
  2. 2. Piecewise Functions 01 01 )( 2 xx xx xf “Pieces of the Function” Domain of each piece A single function, f
  3. 3. Evaluating Piecewise 01 01 )( 2 xx xx xf )2(f )0(f )4(f
  4. 4. Piecewise Functions 14 132 )( xx xx xf
  5. 5. Absolute Value Function xxf )( Can also be expressed as: 0 0 )( xx xx xf
  6. 6. Absolute Value Function 0 0 )( xx xx xf Domain?
  7. 7. Graphing Functions Method 1: Plotting Points (T-Chart) 3)( xxg Find the domain of the function, bef ore making the T-Chart
  8. 8. Graphing Functions Method 1: Plotting Points (T-Chart) 3)( xxg
  9. 9. Graphing Functions Method 1: Plotting Points (T-Chart) xxf 2)(
  10. 10. Reading Graphs of Functions (Similar to what we’ve already done) 1 2 3 4 1 2 3 4 )(xf )2(f )1(f )2(f )4(f
  11. 11. Reading Graphs of Functions (Similar to what we’ve already done) 1 2 3 4 1 2 3 4 )(xf xxf ,3)( xxf ,0)(
  12. 12. Positive / Negative Functions 1 2 3 4 1 2 3 4 )(xf 0)(xf 0)(xf
  13. 13. Positive/Negative Functions Without a graph: The Sign Test Sign Test • Identify zero(s) of the function • Plot the zero(s) on a real number line • Choose a test point in each interval • Evaluate function at each test point to determine the sign of f(x) on each interval
  14. 14. Positive/Negative Functions Without a graph: The Sign Test 0)(th 0)(th 824)( xth Find Intervals Where:
  15. 15. Increasing / Decreasing Functions 1 2 3 4 1 2 3 4 )(xf .)( incxf .)( decxf
  16. 16. Graphing Functions Determining if a graph is a function The Vertical Line Test This is a visual representation of what we did yesterday…Each input cannot have more than one output (not predictable)
  17. 17. Determining if a graph is a function The Vertical Line Test
  18. 18. Classwork • Go over worksheet as class

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