Family of Functions A set of functions whose
- Slides: 10
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.
Parent Function: For all linear functions, the parent function is f(x) = x y =1 x + 0 1 m =1 b =0
Transformation: The graphs of all other linear functions are transformations of the ______ graph of the parent f(x) = x function, ____.
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.
Ex 2: Graph f(x) = -3 x and g(x) = -3 x + 3. Then describe the transformation from the graph of f(x) to the graph of g(x). f(x) = -3 x m = -3 b = 0 g(x) = -3 x + 3 m = -3 b =3 The graph of g(x) is the result of translating the graph of f(x), 3 units up.
Ex 3: Graph f(x) = 2 x + 2 and g(x) = 2 x - 2. Then describe the transformation from the graph of f(x) to the graph of g(x). f(x) = 2 x + 2 m =2 b = 2 g(x) = 2 x - 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 f(x)=mx+b a _____ translation will have the slopes (m) but same _____ (b) different y-intercepts ______.
Parent Function: For all linear functions, the parent function is f(x) = x y =1 x + 0 1 m =1 b =0
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 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.
Ex 3: Graph f(x) = 2 x + 2 and g(x) = 2 x - 2. Then describe the transformation from the graph of f(x) to the graph of g(x). f(x) = 2 x + 2 m =2 1 b = 2 g(x) = 2 x - 2 2 m = 1 b = -2 The graph of g(x) is the result of translating the graph of f(x), 4 units down.
- Total set awareness set consideration set
- Training set validation set test set
- Bounded set vs centered set
- Fucntions
- Crisp set vs fuzzy set
- Crisp set vs fuzzy set
- What is the overlap of data set 1 and data set 2?
- Surjective vs injective
- Difference between nuclear family and joint family
- Periodic table staircase
- Characteristics of single parent family