1 / 10

Transformation: A change in position or size of a figure.

Family of Functions: A set of functions whose graphs have basic characteristics in common. For example, all linear functions form a family because all of their graphs are the same basic shape, which is a line.

barbaramedina
Download Presentation

Transformation: A change in position or size of a figure.

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. Family of Functions: A set of functions whose graphs have basic characteristics in common. For example, all linear functions form a family because all of their graphs are the same basic shape, which is a line. Linear Parent Function: The most basic function in a family. For linear functions, the parent function is y = x or f(x) = x. Transformation:A change in position or size of a figure.

  2. Parent Function: For all linear functions, the parent function is f(x) = x. f(x) = x y = x y =1x + 0 1 m = 1 b = 0

  3. Transformation: The graphs of all other linear functions are ____________ of the graph of the parent function, ________. transformations f(x) = x

  4. Ex 1: Graph f(x) = x and g(x) = x – 5. Then describe the transformation from the graph of f(x) to the graph of g(x). f(x) = x m = 1 b = 0 g(x) = x - 5 m = 1 b = -5 The graph of g(x) is the result of translating the graph of f(x), 5 units down.

  5. Ex 2: Graph f(x) = -3x and g(x) = -3x + 3. Then describe the transformation from the graph of f(x) to the graph of g(x). f(x) = -3x m = -3 b = 0 g(x) = -3x + 3 m = -3 b = 3 The graph of g(x) is the result of translating the graph of f(x), 3 units up.

  6. Ex 3: Graph f(x) = 2x + 2 and g(x) = 2x - 2. Then describe the transformation from the graph of f(x) to the graph of g(x). f(x) = 2x + 2 m = 2 b = 2 g(x) = 2x - 2 m = 2 b = -2 The graph of g(x) is the result of translating the graph of f(x), 4 units down.

  7. So in a linear function __________ a translation will have the same _________ but different ___________. f(x)=mx+b slopes (m) y-intercepts (b)

  8. Parent Function: For all linear functions, the parent function is f(x) = x. f(x) = x y = x y =1x + 0 1 m = 1 b = 0

  9. Ex 1: Graph f(x) = x and g(x) = x – 5. Then describe the transformation from the graph of f(x) to the graph of g(x). f(x) = x 1 m = 1 b = 0 g(x) = x - 5 1 m = 1 b = -5 The graph of g(x) is the result of translating the graph of f(x), 5 units down.

  10. Ex 3: Graph f(x) = 2x + 2 and g(x) = 2x - 2. Then describe the transformation from the graph of f(x) to the graph of g(x). f(x) = 2x + 2 2 m = 1 b = 2 g(x) = 2x - 2 2 m = 1 b = -2 The graph of g(x) is the result of translating the graph of f(x), 4 units down.

More Related