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Absolute Value Functions & Graphs - Module 4 and 5
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Absolute Value Functions & Graphs - Module 4 and 5

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  • This is section 2-5 in the text.
  • Transcript

    • 1. Absolute Value Functions & Graphs Parent function of Abs. Functions y = |x|
    • 2. Absolute Value Functions
      • Spin on linear equations
      • V-shaped graph
      • Has a feel of graphing a linear function.
      • All Absolute Value graphs are in the same form:
      • Where b and c will be real numbers.
    • 3. Graphing Absolute Value Functions
      • Three ways to graph:
        • Use a table
        • Use a TI
        • “ Read” the equation.
      • If you can read a linear eqn., you can read an absolute value eqn.
    • 4. Using a Table
      • The table method works for every two-variable equation in the world.
      • Choose an x-value
      • Sub in the value for x
      • Simplify
      • Your answer is the y-value and now you’ve found a point on the graph.
      • Repeat for 2-4 more x-values and sketch the function.
      • There’s just one problem…
    • 5. The Vertex
      • Abs. Value graphs have two directions.
      • Plot vertex first!!
      • The vertex for ALL Abs. Value functions is at:
    • 6. Example 1
      • Graph
      1. Identify b and c b= 1 c= -2 2. Find the vertex x= y = -2 3. Choose two x-values greater than the x coord. of the vertex and two less than. Lets choose -4,-2, 1, 2. x |x+1| -2 y -4 |-4 + 1| - 2 1 -2 |-2 + 1| - 2 -1 1 | 1 + 1| - 2 0 2 | 2 + 1| - 2 1 4. Set up a table
    • 7. Using the TI: Get your Calc!
      • Make sure the function is solved for y.
      • Hit the ‘y=‘ button
      • Clear out any “old” functions
      • Hit ‘math’ -> move over to ‘num’ -> hit enter
      • Abs( says “take the absolute value of the expression in the parenthesis.
      • Enter the expression and close the parenthesis.
      • If there’s a ‘c’, put it in
      • Hit graph and there it is!
      • Hopefully…if not, hit ‘zoom’ and choose zoomfit or zoomstd
    • 8. Example 2
      • Go to into ‘y=‘
      Graph:
    • 9. Example 2
      • Go to into ‘y=‘
      • ‘ math’ -> move over to ‘num’ -> hit enter
      Graph:
    • 10. Example 2
      • Go to into ‘y=‘
      • ‘ math’ -> move over to ‘num’ -> hit enter
      • Enter the expression ‘x-3’
      • Close parenthesis!!!!!
      Graph:
    • 11. Example 2
      • Go to into ‘y=‘
      • ‘ math’ -> move over to ‘num’ -> hit enter
      • Enter the expression ‘x-3’
      • Close parenthesis!!!!!
      • Then put in +2
      Graph:
    • 12. Example 2
      • Go to into ‘y=‘
      • ‘ math’ -> move over to ‘num’ -> hit enter
      • Enter the expression ‘x-3’
      • Close parenthesis!!!!!
      • Then put in +2
      • Hit Graph
      • Zoom, if needed
      Graph:
    • 13. “ Read the Equation”
      • The ‘c’ on the outside of the bars moves the parent function up/down.
        • Positive is up, negative is down.
      • The ‘b’, the constant on the inside of the abs. value bars moves the parent function left/right the OPPOSITE of what you see.
        • Positive goes left and negative goes right.
      • To flip the V upside-down, there must be a negative number multiplied on the outside of the bars.
    • 14. Example 3
      • Graph:
      • Place Parent Function
    • 15. Example 3
      • Graph:
      • Place Parent Function
      • Move left or right– here we’ll go left to -5
    • 16. Example 3
      • Graph:
      • Place Parent Function
      • Move left or right– here we’ll go left to -5
      • Move up or down– here we’ll go down to -2
      • Done 