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2.4 Use Absolute Value Functions and Transformations

2.4 Use Absolute Value Functions and Transformations. 2.4-2.5 Quiz: Friday. Vocabulary. The function f(x) = |x| is an absolute value function . The highest of lowest point on the graph of an absolute value function is called the vertex .

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2.4 Use Absolute Value Functions and Transformations

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  1. 2.4Use Absolute Value Functions and Transformations 2.4-2.5 Quiz: Friday

  2. Vocabulary • The function f(x) = |x| is an absolute value function. • The highest of lowest point on the graph of an absolute value function is called the vertex. • An axis of symmetry of the graph of a function is a vertical line that divides the graph into mirror images. • An absolute value graph has one axis of symmetry that passes through the vertex.

  3. Absolute Value Function • Vertex • Axis of Symmetry

  4. Vocabulary • The zeros of a function f(x) are the values of x that make the value of f(x) zero. • On this graph where x = -3 and x = 3 are where the function would equal 0. f(x) = |x| - 3

  5. Vocabulary • A transformation changes a graph’s size, shape, position, or orientation. • A translation is a transformation that shifts a graph horizontally and/or vertically, but does not change its size, shape, or orientation. • When a = -1, the graph y = a|x| is a reflection in the x-axis of the graph of y = |x|.

  6. 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)

  7. 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

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

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

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

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

  12. Example 4: • The graph of a function y = f(x) is shown. Sketch the graph of the given function • y = -f(x – 1) + 2 • y = ½ f(x)

  13. You Try: • The graph of a function y = f(x) is shown. Sketch the graph of the given function • y = f(x – 3) + 2 • y = 2 f(x)

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