LEARNING GOALS FOR LESSON 2.6 Stretches/Compressions

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Presentation transcript:

LEARNING GOALS FOR LESSON 2.6 Stretches/Compressions Recognize sketch and write transformations of linear functions including (1) translation, (2) reflection, (3) stretch/compression and (4) combination of transformations. Translations Horizontal Vertical Reflections X-axis Y-axis Stretches/Compressions

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 f(x) Rule: g(x) B. f(x) = 3x + 1; horizontal translation 2 units right LG 2.6.1 f(x) Rule: g(x) C. f(x) = 3x + 1; vertical translation 5 units up LG 2.6.1 f(x) Rule: g(x)

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 x –2 2 f(x) 1 Stretches and compressions change the _____ of a linear function. If the line becomes. . . STEEPER: stretched __________ or compressed ___________ FLATTER: compressed _________ or stretched _____________ These don’t change! y–intercepts in a horizontal stretch or compression x–intercepts in a vertical stretch or compression Helpful Hint

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. f(x) Rule: g(x) 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. f(x) Rule: g(x)

Ex 3: Combining Transformations of Linear Functions LG 2.6.4 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. f(x) Rule: g(x) h(x) Let g(x) be a vertical compression of f(x) = x by a factor of ½ followed by a horizontal shift 8 left units. Write the rule for g(x). f(x) Rule: g(x) h(x)