Family of Functions: A set of functions whose graphs have basic characteristics in common. For example, all linear functions form a family because all.

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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.

Notes on Transforming Linear Functions #1 Parent Function: For all linear functions, the parent function is f(x) = x. 11/11/2014 f(x) = x y = x y =1x + 0 1 m = 1 b =

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

f(x) = x m = 1 b = g(x) = x - 5 m = 1 b = -5 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 = 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.

f(x) = -3x m = -3 b = g(x) = -3x + 3 m = -3 b = 3 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 = 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.

f(x) = 2x + 2 m = 2 b = 2 g(x) = 2x - 2 m = 2 b = -2 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.

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

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

f(x) = x 1 m = 1 b = g(x) = x - 5 1 m = 1 b = -5 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 = 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.

f(x) = 2x + 2 2 m = 1 b = 2 g(x) = 2x - 2 2 m = 1 b = -2 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.