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Section 2.7

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

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  1. Section 2.7 Use Absolute Value Functions and Transformations Read all of p. 123.

  2. 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.

  3. Read about stretches, shrinks, and reflections on p. 124.

  4. 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.

  5. Read 1st paragraph on p. 125.

  6. 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.

  7. Example 4 • A landscaper sketches the design for a triangular shrub protector on graph paper. Write an equation for the shrub protector.

  8. 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.

  9. Example 5 • The graph of a • function y = f (x) is • shown. Sketch the • graph of the given • function.

  10. 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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