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Graphing Piecewise, Step, and Absolute Value Functions

Learn how to graph piecewise, step, and absolute value functions, and understand the vocabulary and common parent functions. Explore translations of graphs and practice writing equations for given graphs.

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Graphing Piecewise, Step, and Absolute Value Functions

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  1. WARMUP 1-7 ANY ANY

  2. 1-7Graphing Functions Piece-wise functions Absolute Value Functions Greatest Integer Functions (Step)

  3. Lesson 1-7 Piecewise Functions What does a piecewise, step and absolute value function look like? Vocabulary • Piecewise function • Step function • Greatest integer function • Absolute value function

  4. Common “Parent” Functions • Sketch the graph of each of the following making sure to include the following: • Equation of graph • Label x and y-axes • Indicate scale on each axis y = x y = x2 y = x3 y = | x | Linear quadratic cubic absolute value

  5. Greatest Integer Function • y = [x] • Returns the greatest integer value less than or equal to x.

  6. Translation of graphs (shifting graphs.) • Addition and subtraction changes the position of a graph. • Multiplication and division changes the shape of a graph. • Graph the following without your calculator first by guessing the translation. • y = |x| + 2 • y = |x| - 1 • y = |x + 1| • y = |x – 2| • y = |x + 3| - 1 • y = - |x| + 1

  7. Practice • Write the equation for the following graph:

  8. Guided Practice

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