MM2A1. Students will investigate step and piecewise functions, including greatest integer and absolute value functions.

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Standard

• MM2A1. Students will investigate step and
  piecewise functions, including greatest integer
  and absolute value functions.
• b. Investigate and explain characteristics of a
  variety of piecewise functions including domain,
  range, vertex, axis of symmetry, zeros,
  intercepts, extrema, points of discontinuity,
  intervals over which the function is constant,
  intervals of increase and decrease, and rates of
  change.
• c. Solve absolute value equations and
  inequalities analytically, graphically, and by
  using appropriate technology.

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Absolute Value Functions
General Form y a x h k
Characteristics
1. The graph is V-shaped

• Vertex of the graph (h, k)
• note opposite of h in general form

• a acts as the slope for the right hand side
  (the left side is the opposite)

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Absolute Value Functions
Parent Graph y x x y ordered pair
Graph Transformations
What effect does each one have on the parent
graph? y a x h k
Moves the graph up () or down (-)
Determines if graph is fatter 0 lt a lt 1 or
skinnier a gt 1
Moves the graph left () or right (-)
Determines if graph opens up () or down (-)
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Determine the vertex of the following functions.
State whether the graph will open up or down.

1. y 2 x - 2 3 4. y 1/3 x 5
2. y -x 5 - 6 5. y x
3. y -2x 2

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Steps for Graphing

• Find and plot the vertex (opposite of h, k)
• Find and sketch the axis of symmetry
• Use a to find the slope and the next 2 points.
• 4) Using symmetry, plot 2 additional points and
  connect them to your vertex to create a V
  shaped graph!

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Graphing Absolute Value Functionsexample 1
Vertex ( , ) Slope ________
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Graphing Absolute Value Functionsexample 2
Vertex ( , ) Slope ________
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Graphing Absolute Value Functionsexample 3
Vertex ( , ) Slope ________
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Steps for writing an equation when given an
absolute value graph.

1. Identify the vertex (opposite of h, k)
2. Determine if a will be positive or negative
   (opens up or down)
3. Find a point to the right of the vertex that the
   graph passes through exactly and count the slope
   from the vertex to the point. This is a (the
   slope!)
4. For the final answer substitute a and the
   vertex (opposite of h, k) back into

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Example 1
Vertex ( , ) A is positive /
negative Slope ________ Equation y

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Example 2
Vertex ( , ) A is positive /
negative Slope ________ Equation y