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LEARNING GOALS FOR LESSON 2.9

Remember!. The general forms for translations are Vertical: g ( x ) = f ( x ) + k Horizontal: g( x ) = f ( x – h ). LEARNING GOALS FOR LESSON 2.9. Write, graph and transform absolute-value functions including (1) translations, (2) reflections, and (3) stretches/compressions.

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LEARNING GOALS FOR LESSON 2.9

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  1. Remember! The general forms for translations are Vertical: g(x) = f(x) + k Horizontal: g(x) = f(x– h) LEARNING GOALS FOR LESSON 2.9 Write, graph and transform absolute-value functions including (1) translations, (2) reflections, and (3) stretches/compressions. The graph of the parent absolute-value function f(x) = |x| has a V shape with a minimum point or vertex at (0, 0).

  2. Example 1A: Translating Absolute-Value Functions LG 2.9.1 Perform the transformation on f(x) = |x|. Then graph the transformed function g(x). Write the new equation and tell what the vertex is. 5 units down Example 1B: Translating Absolute-Value Functions LG 2.9.1 Perform the transformation on f(x) = |x|. Then graph the transformed function g(x). 1 unit left The vertex of g(x) is (___, ___)

  3. Example 1C: Translations of an Absolute-Value Function LG 2.9.1 Translate f(x) = |x| so that the vertex is at (–1, –3). Then graph. Check Yourself! Translate f(x) = |x| so that the vertex is at (4, –2). Then graph.

  4. Remember! Reflection across x-axis: g(x) = –f(x) Reflection across y-axis: g(x) = f(–x) g f Remember! Vertical stretch and compression : g(x) = af(x) Horizontal stretch and compression: g(x) = f Absolute-value functions can also be stretched, compressed, and reflected. LG 2.9.2 Perform the transformation. Then graph. Reflect the graph. f(x) =|x –2| + 3 across the y-axis. LG 2.9.3

  5. Stretch the graph. f(x) = |x| – 1 vertically by a factor of 2.

  6. Compress the graph of f(x) = |x + 2| – 1 horizontally by a factor of . Example 3C: Transforming Absolute-Value Functions LG 2.9.1 Check Yourself! Perform the transformation. Then graph. Reflect the graph. f(x) = –|x – 4| + 3 across the y-axis.

  7. Lesson Quiz: Part I Perform each transformation. Then graph. 1. Translate f(x) = |x| 3 units right. 2. Translate f(x) = |x| so the vertex is at (2, –1). 3. Stretch the graph of f(x) = |2x| – 1 vertically by a factor of 3 and reflect it across the x-axis.

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