Absolute value functions

Absolute value functions

• 1.
  2.8 Absolute ValueFunctions
• 2.
  Absolute Value isdefined by:
• 3.
  The graph ofthis 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.
  y = a |x - h| + k Vertex is @ (h,k) & is symmetrical in the line x=h V-shaped If a< 0 the graph opens down (a is negative) If a>0 the graph opens up (a is positive) The graph is wider if |a| < 1 (fraction < 1) The graph is narrower if |a| > 1 a is the slope to the right of the vertex (…-a is the slope to the left of the vertex)
• 5.
  To graph y= a |x - h| + k 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.) Use the slope to plot another point to the RIGHT of the vertex. Use symmetry to plot a 3 rd point Complete the graph
• 6.
  Graph y =- |x + 2| + 3 V = (-2,3) Apply the slope a=-1 to that point Use the line of symmetry x=-2 to plot the 3rd point. Complete the graph
• 7.
  Graph y =- |x - 1| + 1
• 8.
  Write the equationfor:
• 9.
  The vertex is@ (0,-3) It has the form: y = a |x - 0| - 3 To find a: substitute the coordinate of a point (2,1) in and solve (or count the slope from the vertex to another point to the right) Remember: a is positive if the graph goes up a is negative if the graph goes down So the equation is: y = 2 |x| -3
• 10.
  Write the equationfor: y = ½ |x| + 3
• 11.
  Assignment