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LEARNING GOALS FOR LESSON 2.6

LEARNING GOALS FOR LESSON 2.6. Recognize sketch and write transformations of linear functions including (1) translation, (2) reflection, (3) stretch/compression and (4) combination of transformations. Example 1: Translating & Reflecting Linear Functions.

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LEARNING GOALS FOR LESSON 2.6

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  1. LEARNING GOALS FOR LESSON 2.6 Recognize sketch and write transformations of linear functions including (1) translation, (2) reflection, (3) stretch/compression and (4) combination of transformations.

  2. Example 1: Translating & Reflecting Linear Functions Let g(x) be the indicated transformation of f(x). Write the rule for g(x). A. f(x) = x – 2 , horizontal translation 3 right LG 2.6.1 B. f(x) = 3x + 1; horizontal translation 2 units right LG 2.6.1 C. f(x) = 3x + 1; vertical translation 5 units up LG 2.6.1

  3. Helpful Hint • These don’t change! • y–intercepts in a horizontal stretch or compression • x–intercepts in a vertical stretch or compression Example 1B: Translating Reflecting Functions LG 2.6.2 Write the rule for g(x). The following is a linear function defined in the table; Reflect across x-axis Stretches and compressions change the _____ of a linear function. If the line becomes. . . STEEPER: stretched __________ or compressed ___________ FLATTER: compressed _________ or stretched _____________

  4. Example 2: Stretching & Compressing Linear Functions LG 2.6.3 Let g(x) be a horizontal compression of f(x) = –x + 4 by a factor of ½. Write the rule for g(x), and graph the function. Let g(x) be a vertical compression of f(x) = 3x + 2 by a factor of ¼. Write the rule for g(x) and graph the function.

  5. LG 2.6.4 Ex 3: Combining Transformations of Linear Functions Let g(x) be a horizontal shift of f(x) = 3x left 6 units followed by a horizontal stretch by a factor of 4. Write the rule for g(x). Step 1 First perform the translation. Step 2 Then perform the stretch. Let g(x) be a vertical compression of f(x) = x by a factor of ½followed by a horizontal shift 8 leftunits. Write the rule for g(x).

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