2.8 Absolute Value Functions

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2.8 Absolute Value Functions

  1. 1. 2.8 Absolute Value Functions
  2. 2. Absolute Value Functions• The absolute value of x is defined by:• The graph of y = |x| looks like a v-shape. vertex
  3. 3. Why are they important?• Have you ever played pool or putt-putt golf?• The path of the ball when making a bank shot is an example of an absolute value function.
  4. 4. Transformations• There are four ways the absolute value graph can be changed:1. Open Up or Open Down2. Change in Width – sides can be steeper or less steep3. Horizontal Shift – vertex moves left or right4. Vertical Shift- vertex moves up or down
  5. 5. General Form• y = a |x – h| + k• Effects of a:• When a > 0 (positive), the V opens up.• When a < 0 (negative), the V opens down.• When |a| < 1, the sides are less steep than y = |x|.• When |a| > 1, the sides are steeper than y = |x|.
  6. 6. ExamplesNotice:a is the slope of the right side of the graph!
  7. 7. Effect of h y = a |x – h| + k• h shifts the vertex left or right• The direction is opposite the sign of h• Examples:
  8. 8. Effects of k y = a |x – h| + k• k shifts the vertex up or down• Positive k shifts up• Negative k shifts down• Examples:
  9. 9. The Vertex• The vertex will be at (h, k).• Example:• Vertex: (-3, -4)• Axis of symmetry: Vertical line through the vertex (-3, -4)
  10. 10. Your Turn!• Find the vertex:
  11. 11. Graphing Absolute Value Functions• Plot the vertex.• Sketch the axis of symmetry.• Use a (the slope) to graph the right side.• Use symmetry to draw in the left side.• Example:Graph
  12. 12. Example:• Graph
  13. 13. Your Turn!• Graph
  14. 14. Example:• Graph
  15. 15. Your Turn!• Graph
  16. 16. Writing Absolute Value Functions• y = a| x – h | + k• Find the vertex (h, k)• Count the slope (of the right side) to find a.
  17. 17. Example:• Write an equation of the graph shown.
  18. 18. Your Turn!• Write an equation of the graph shown.

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