1 / 8

Reflection across x -axis: g ( x ) = – f (x) Reflection across y -axis: g(x) = f ( – x )

An absolute-value function is a function whose rule contains an absolute-value expression. The graph of the parent absolute-value function f ( x ) = | x | has a V shape with a minimum point or vertex at (0, 0).

markchung
Télécharger la présentation

Reflection across x -axis: g ( x ) = – f (x) Reflection across y -axis: g(x) = f ( – x )

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. An absolute-value function is a function whose rule contains an absolute-value expression. The graph of the parent absolute-value function f(x) = |x| has a V shape with a minimum point or vertex at (0, 0). The absolute-value parent function is composed of two linear pieces, one with a slope of –1 and one with a slope of 1. In Lesson 2-6, you transformed linear functions. You can also transform absolute-value functions.

  2. Remember! Remember! Remember! Reflection across x-axis: g(x) = –f(x) Reflection across y-axis: g(x) = f(–x) Vertical stretch and compression : g(x) = af(x) Horizontal stretch and compression: g(x) = f The general forms for translations are Vertical: g(x) = f(x) + k Horizontal: g(x) = f(x– h)

  3. Ex 1A: Perform the transformation on f(x) = |x|. Then graph the transformed function g(x). 5 units down f(x) = |x| g(x) = f(x) + k The graph of g(x) = |x| – 5 is the graph of f(x) = |x| after a vertical shift of 5 units down. The vertex of g(x) is (0, –5). g(x) = |x| – 5 The graph of g(x) = |x|– 5 is the graph of f(x) = |x| after a vertical shift of 5 units down. The vertex of g(x) is (0, –5). f(x) g(x)

  4. Ex 1B: Perform the transformation on f(x) = |x|. Then graph the transformed function g(x). 1 unit left f(x) = |x| g(x) = f(x– h) g(x) = |x – (–1)| = |x + 1| The graph of g(x) = |x + 1| is the graph of f(x) = |x| after a horizontal shift of 1 unit left. The vertex of g(x) is (–1, 0). f(x) g(x)

  5. Because the entire graph moves when shifted, the shift from f(x) = |x| determines the vertex of an absolute-value graph. Ex 2: Translate f(x) = |x|so that the vertex is at (–1, –3). Then graph. g(x) = |x – h| + k g(x) = |x – (–1)| + (–3) f(x) g(x) = |x + 1| – 3 The graph of g(x) = |x + 1| – 3 is the graph of f(x) = |x| after a vertical shift down 3 units and a horizontal shift left 1 unit. g(x) The graph confirms that the vertex is (–1, –3).

  6. g f Ex 3A: Perform the transformation. Then graph. Reflect the graph. f(x) =|x –2| + 3 across the y-axis. Take the opposite of the input value. g(x) = f(–x) g(x) = |(–x) – 2| + 3 The vertex of the graph g(x) = |–x – 2| + 3 is (–2, 3).

  7. f(x) g(x) Ex 3B: Stretch the graph. f(x) = |x| – 1 vertically by a factor of 2. g(x) = af(x) g(x) = 2(|x| – 1) Multiply the entire function by 2. g(x) = 2|x| – 2 The graph of g(x) = 2|x| – 2 is the graph of f(x) = |x| – 1 after a vertical stretch by a factor of 2. The vertex of g is at (0, –2).

  8. g Substitute for b. Compress the graph of f(x) = |x + 2| – 1 horizontally by a factor of . Ex 3C: Simplify. g(x) = |2x + 2| – 1 The graph of g(x) = |2x + 2|– 1 is the graph of f(x) = |x + 2| – 1 after a horizontal compression by a factor of . The vertex of g is at (–1, –1). f

More Related