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Published byMeryl Sherman Modified over 4 years ago

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**2.4 Use Absolute Value Functions and Transformations**

Quiz: Friday

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**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.

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**Absolute Value Function**

Vertex Axis of Symmetry

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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

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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|.

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**y = -a |x – h| + k Transformations**

*Remember that (h, k) is your vertex* Reflection across the x-axis Vertical Translation Vertical Stretch a > 1 (makes it narrower) OR Vertical Compression 0 < a < 1 (makes it wider) Horizontal Translation (opposite of h)

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**Example 1: Identify the transformations: y = 3 |x + 2| - 3**

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**Example 2: Graph y = -2 |x + 3| + 2. What is your vertex?**

What are the intercepts? What are the zeros?

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**You Try: Graph y = -1/2 |x – 1| - 2**

Compare the graph with the graph of y = |x| (what are the transformations)

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Example 3: Write a function for the graph shown.

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You Try: Write a function for the graph shown.

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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)

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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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