College Algebra 2.3
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College Algebra 2.3

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College Algebra 2.3 College Algebra 2.3 Presentation Transcript

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