1. 3.2 Linear Functions

2. Vocabulary Linear Equation in two variables (x and y):
An equation that can be written in the form y = mx + b, where m and b are constants.
Linear Function:
A function whose graph forms a non-vertical line.
A linear functions has a constant rate of change.
Nonlinear Function:
A function that does not have a constant rate of change.
It’s graph does not form a line.

3. Identifying Linear Functions Using Graphs Does the graph represent a linear or nonlinear function? Explain. Example 1:
This is a nonlinear function since it’s graph does not form a line.
This is a linear function since it’s graph forms a line.

4. Identifying Linear Functions Using Tables Does the table represent a linear or nonlinear function? Explain. Example 2: +3 +3 +3 a. x 3 6 9 12 y 36 30 24 18
As x increases by 3, y decreases by 6. The rate of change is constant. So, the function is linear. -6 -6 -6 +2 +2 +2 x 1 3 5 7 y 2 9 20 35 b.
As x increases by 2, y increases by different amounts. The rate of change is not constant. So, the function is nonlinear. +7
+11
+15

5. You try! Are the following linear or nonlinear functions? Explain.
Since this graph does not form a line it is a nonlinear function.
Since this graph forms a line it is a linear function.
As x increases by 1, y increases by 2. The rate of change is constant so this is a linear function.
As x increases by 1, y decreases by different amounts. The rate of chance is not constant so this is a nonlinear function.

6. Identifying Linear Functions Using Equations Which of the following represents a linear function? Example 3:

7. Graphing Linear Functions
Solution to a Linear Equation in Two Variables
The solution is an ordered pair (x, y) that makes the equation true.
Discrete Domain
A discrete domain is a set of input values that consist of only certain numbers in an interval
Continuous Domain
Continuous domain is a set of input values that consists of all numbers in an interval.

8. Graphing Discrete Data Example 4:
The linear function y = 15.95x represents the cost (y) in dollars of (x) tickets for a museum. Each customer can buy a maximum of 4 tickets.
Find the domain of the function.
Since you can not buy part of a ticket the domain must be a whole number. The maximum tickets that can be purchased is 4. The domain would be: 0, 1, 2, 3, 4

9. Graphing Discrete Date Example 4:
The linear function y = 15.95x represents the cost (y) in dollars of (x) tickets for a museum. Each customer can buy a maximum of 4 tickets. b) Graph the function using the domain.

10. Graphing Continuous Data Example 5:
A cereal bar contains 130 calories. The number c of calories consumed is a function of the number b of bars eaten.
Does this represent a linear function?
Yes, as b increases by 1, c will increase by 130. The rate of change is constant.
b) Find the domain of the function. Is the domain discrete or continuous? Explain.
You can eat part of a cereal bar. The number b can be any value greater than or equal to 0. The domain is b>0 and it is continuous.
c) Graph the function using its domain.

11. Graphing Continuous Data Example 5:
A cereal bar contains 130 calories. The number c of calories consumed is a function of the number b of bars eaten. c) Graph the function using its domain.

12. You try! Is the domain discrete or continuous? Explain.
Input
Number of stories, x 1 2 3
Output
Height of building (feet), y 12 24 36
The domain is the number of stories. Since there can not be partial stories in a building, the domain must be a whole number. The domain is discrete.

13. Writing Real-Life Problems Example 6:
Write a real life problem to fit the data shown in each graph. Is the domain in each function discrete or continuous? Explain.