Absolute value functions

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Absolute value functions

  1. 1. 2.8 Absolute Value Functions
  2. 2. Absolute Value is defined by:
  3. 3. The graph of this piecewise function consists of 2 rays, is V-shaped and opens up. To the left of x=0 the line is y = -x To the right of x = 0 the line is y = x Notice that the graph is symmetric in the y-axis because every point (x,y) on the graph, the point (-x,y) is also on it.
  4. 4. y = a |x - h| + k <ul><li>Vertex is @ (h,k) & is symmetrical in the line x=h </li></ul><ul><li>V-shaped </li></ul><ul><li>If a< 0 the graph opens down (a is negative) </li></ul><ul><li>If a>0 the graph opens up (a is positive) </li></ul><ul><li>The graph is wider if |a| < 1 (fraction < 1) </li></ul><ul><li>The graph is narrower if |a| > 1 </li></ul><ul><li>a is the slope to the right of the vertex </li></ul><ul><li>(…-a is the slope to the left of the vertex) </li></ul>
  5. 5. To graph y = a |x - h| + k <ul><li>Plot the vertex (h,k) (set what’s in the absolute value symbols to 0 and solve for x; gives you the x-coord. of the vertex, y-coord. is k.) </li></ul><ul><li>Use the slope to plot another point to the RIGHT of the vertex. </li></ul><ul><li>Use symmetry to plot a 3 rd point </li></ul><ul><li>Complete the graph </li></ul>
  6. 6. Graph y = - |x + 2| + 3 <ul><li>V = (-2,3) </li></ul><ul><li>Apply the slope a=-1 to that point </li></ul><ul><li>Use the line of symmetry x=-2 to plot the 3rd point. </li></ul><ul><li>Complete the graph </li></ul>
  7. 7. Graph y = - |x - 1| + 1
  8. 8. Write the equation for:
  9. 9. <ul><li>The vertex is @ (0,-3) </li></ul><ul><li>It has the form: </li></ul><ul><li>y = a |x - 0| - 3 </li></ul><ul><li>To find a: substitute the coordinate of a point (2,1) in and solve </li></ul><ul><li>(or count the slope from the vertex to another point to the right) </li></ul><ul><li>Remember: a is positive if the graph goes up </li></ul><ul><li>a is negative if the graph goes down </li></ul>So the equation is: y = 2 |x| -3
  10. 10. Write the equation for: y = ½ |x| + 3
  11. 11. Assignment

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