Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Absolute Value Functions & Graphs

28,847 views

Published on

  • Be the first to like this

Absolute Value Functions & Graphs

  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><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:
  9. 9. “ 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>
  10. 10. 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>

×