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. 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 =

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

4. 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.

5. f(x) = -3x m = -3 b = g(x) = -3x + 3 m = -3 b = 3
Ex 2: Graph f(x) = -3x and g(x) = -3x 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.

6. 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 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.
y = x
y =1x + 0 1
m = 1
b =

9. 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.

10. 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 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.