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# Absolute Value Functions & Graphs - Module 4 and 5

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• This is section 2-5 in the text.
• ### Absolute Value Functions & Graphs - Module 4 and 5

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