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Section 2.7. Use Absolute Value Functions and Transformations. Read all of p. 123. Example 1. Graph y = | x – 1 | + 3. Compare the graph with the graph of y = | x |. Comparison y = | x – 1 | + 3 translate y = | x | one unit to the right and three units up.

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Section 2 7
Section 2.7

Use Absolute Value Functions and Transformations

Read all of p. 123.


Example 1
Example 1

  • Graph y = | x – 1 | + 3. Compare the graph with the graph of y = | x |.

  • Comparison

  • y = | x – 1 | + 3 translate y = | x | one unit to the right and three units up.



Example 2
Example 2

  • Compare each graph with the graph y = | x |.

  • Comparison

  • (a) y = 1/3|x | is the graph of y = | x | vertically shrunk by a factor of 1/3

  • (b) y = -2|x| is the graph of y = | x | vertically stretched by a factor of 2 and reflected over the x-axis.


Read 1st paragraph on p. 125.


Example 3
Example 3

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

  • Comparison

  • The graph of y = ¼| x + 3 | − 2 is the graph of

  • y = | x |first vertically shrunk by a factor of ¼ then translated 3 units to the left and 2 units down.


Example 4
Example 4

  • A landscaper sketches the design for a triangular shrub protector on graph paper. Write an equation for the shrub protector.


The vertex is (5, 6).

A point on the graph is either (0, 0) or (10, 0). Now solve for a.

Read 1st paragraph and

key concept on p. 126.


Example 5
Example 5

  • The graph of a

  • function y = f (x) is

  • shown. Sketch the

  • graph of the given

  • function.


  • HW:

  • Thursday’s HW: Sections 2.5 and 2.6 Quiz Review

  • Monday’s HW: pp. 127-129 (4-26 even, 32, 36, 38, 40)


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