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Standard

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

charles-donovan
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Standard

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  1. 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.

  2. 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)

  3. 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 < a < 1 or skinnier a > 1 Moves the graph left (+) or right (-) Determines if graph opens up (+) or down (-)

  4. Determine the vertex of the following functions. State whether the graph will open up or down. • y = 2 |x - 2| + 3 4. y = 1/3 |x| + 5 • y = -|x + 5| - 6 5. y = |x| • y = -2|x + 2|

  5. 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!

  6. Graphing Absolute Value Functionsexample 1 Vertex: ( , ) Slope: ________

  7. Graphing Absolute Value Functionsexample 2 Vertex: ( , ) Slope: ________

  8. Graphing Absolute Value Functionsexample 3 Vertex: ( , ) Slope: ________

  9. Steps for writing an equation when given an absolute value graph. • Identify the vertex (opposite of h, k) • Determine if “a” will be positive or negative (opens up or down) • 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!) • For the final answer: substitute “a” and the vertex (opposite of h, k) back into

  10. Example 1 Vertex: ( , ) A is: positive / negative Slope: ________ Equation: y =

  11. Example 2 Vertex: ( , ) A is positive / negative Slope: ________ Equation: y =

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