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Exploring Absolute Value Graph Transformations

Understand absolute value function transformations through reflection, shifts, stretches, compressions, translations, and vertex considerations.

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Exploring Absolute Value Graph Transformations

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  1. Math on the Mind: • Graph y = | x | + 2 and y = | x+ 2|. • Explain the difference between the two graphs.

  2. Absolute Value Graphs Mrs. King Unit 9, Day 2

  3. Graph This Absolute Value Function Reflect graph across the x-axis: f(x) flips the graphs

  4. Graphing Absolute Value Functions Shifts 3 to the right Shifts 2 to the left Shifts 3 to the left Shifts 2 up Shifts 1 up Shifts 2 down Reflect over x-axis Reflect over x-axis

  5. Transformations y = -a |x – h| + k *Remember that (h, k) is your vertex* Reflection across the x-axis Vertical Translation Vertical Stretcha > 1(makes it narrower)ORVertical Compression 0 < a < 1 (makes it wider) Horizontal Translation (opposite of h)

  6. Example 1: • Identify the transformations: • y = 3 |x + 2| - 3 • y = |x – 1| + 2 • y = 2 |x + 3| - 1 • y = -1/3|x – 2| + 1

  7. You Try: • Graph y = |x – 1| - 2 • Compare the graph with the graph of y = |x| (what are the transformations?)

  8. Example 2: • Graph y = -2 |x + 3| + 2. • What transformations are involved? • What is your vertex?

  9. Example 3: • Write a function for the graph shown.

  10. You Try: • Write a function for the graph shown.

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