1. 6.6 Transforming Linear Functions

2. Changing the value of b in f(x) = mx + b causes a change in the y-intercept of the graph of that equation. It translates the graph up or down the y-axis to create parallel lines.
Changing the value of m in f(x) = mx + b causes a change in the slope of the graph of that equation. It rotates the graph on the y-intercept to create lines that are more or less steep.

3. How the Value of m Changes
Effect on the Graph of
f(x) =mx
Increase m when m > 0
Graph becomes steeper.
Decrease m toward 0
when m > 0
Graph becomes less steep.
Decrease m when m < 0
Increase m toward 0 when
m < 0

4. A family of functions is a set of functions whose equations have a similar form. The “parent” of the family is the equation in the family with the simplest form.
For example, f(x) = x is a parent to other functions, such as f(x) = x + 1.
A parameter is one of the constants in a function or equation that determines which variation of the parent function one is considering. In y = mx + b, the parameter m is slope. The parameter b is the y-intercept.

5. 1. A satellite dish company charges a one-time installation fee of $75 and then a monthly usage charge of $40. The total cost C of using that satellite service is described by the function C(t) = 40t + 75, where t is the time (in months) since starting the service. For each situation described below, sketch a graph using the given graph of C(t) = 40t + 75 as a reference. Describe the impact of the changes on the domain and range of the function.
The satellite dish company reduces its one-time installation fee to $60.
b. The satellite dish company decreases its monthly fee to $30.

7. 2. The graph of the function f(x) = x - 2 is shown below.

8. Graph two more functions in the same family for which the parameter being changed is the y-intercept.
Graph two more functions in the same family for which the parameter being changed is the slope.