3 2 Linear Functions Vocabulary Linear Equation in

3. 2 Linear Functions

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.

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.

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

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.

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

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.

Graphing Discrete Date Example 4: The linear function y = 15. 95 x represents the cost (y) in dollars of (x) tickets for a museum. Each customer can buy a maximum of 4 tickets. a) 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

Graphing Discrete Date Example 4: The linear function y = 15. 95 x 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.

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. a) 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.

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.

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.

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.