2 4 use absolute value functions and transformations
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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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2 4 use absolute value functions and transformations

2.4Use Absolute Value Functions and Transformations

2.4-2.5 Quiz: Friday


Vocabulary

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.


2 4 use absolute value functions and transformations

  • Absolute Value Function

  • Vertex

  • Axis of Symmetry


Vocabulary1

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


Vocabulary2

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|.


Transformations

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)


Example 1

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


Example 2

Example 2:

  • Graph y = -2 |x + 3| + 2.

    • What is your vertex?

    • What are the intercepts?

    • What are the zeros?


You try

You Try:

  • Graph y = -1/2 |x – 1| - 2

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

      (what are the transformations)


Example 3

Example 3:

  • Write a function for the graph shown.


You try1

You Try:

  • Write a function for the graph shown.


Example 4

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)


You try2

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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