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2.4 Use Absolute Value Functions and TransformationsPowerPoint Presentation

2.4 Use Absolute Value Functions and Transformations

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2.4 Use Absolute Value Functions and Transformations

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2.4Use Absolute Value Functions and Transformations

2.4-2.5 Quiz: Friday

- 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.

- Absolute Value Function
- Vertex
- Axis of Symmetry

- 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

- 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|.

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)

- Identify the transformations:
- y = 3 |x + 2| - 3
- y = |x – 1| + 2
- y = 2 |x + 3| - 1
- y = -1/3|x – 2| + 1

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

- Graph y = -1/2 |x – 1| - 2
- Compare the graph with the graph of y = |x|
(what are the transformations)

- Compare the graph with the graph of y = |x|

- Write a function for the graph shown.

- Write a function for the graph shown.

- 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)

- 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)