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College Algebra 2.3

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College Algebra 2.3

  1. 1. 2.3 Analyzing Graphs of Functions <ul><li>Vertical Line Test (again) </li></ul><ul><li>Domain and Range from a Graph </li></ul><ul><li>Zeros of a Function </li></ul><ul><li>Intervals where Increasing, Decreasing, or Constant </li></ul>
  2. 2. A. Remember vertical line test? <ul><li>Here it is again: </li></ul>
  3. 3. B. Domain and Range from a Graph <ul><li>Break out the CRAYONS! Or just pretend. </li></ul><ul><li>For the DOMAIN of a graph, imagine a big sunshine over and below it, casting a SHADOW onto the x-axis. </li></ul><ul><li>The domain is usually written in interval notation. </li></ul>
  4. 4. State the domain in interval notation
  5. 5. Now for the Range (shadow on the y-axis)
  6. 6. Find the domain and range:
  7. 7. Find the domain and range:
  8. 8. C. If you’re asked to “find the zeros of the function,” it just means replace “f(x)” with zero and solve. Like these:
  9. 9. D. Finding intervals where increasing, decreasing, or constant. <ul><li>“ INCREASING” = “uphill from left to right” </li></ul><ul><li>“ DECREASING” = “downhill from left to right” </li></ul><ul><li>“ CONSTANT” = “horizontal” </li></ul><ul><li>“ INCREASING” = positive slope </li></ul><ul><li>“ DECREASING” = negative slope </li></ul><ul><li>“ CONSTANT” = zero slope </li></ul>
  10. 10. ALL THESE INTERVALS ARE OPEN! <ul><li>WHEN ASKED TO FIND INTERVALS WHERE DECREASING, INCREASING, CONSTANT, USE OPEN INTERVALS! </li></ul><ul><li>ROUND BRACKETS, NOT SQUARE ONES. </li></ul>
  11. 11. State intervals where increasing, decreasing, or constant:
  12. 12. State intervals where increasing, decreasing, or constant:
  13. 13. State intervals where increasing, decreasing, or constant:
  14. 14. State intervals where increasing, decreasing, or constant:

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