The document defines domain, range, and functions. It provides examples of determining the domain and range of relations and whether relations are functions. It also gives exercises on writing equations and ordered pairs for linear functions based on tables of values.

1. 5.1 Linear Functions and Graphs Student Study Guide

2. Definitions Domain: first coordinates in a set of ordered pairs, x values (3, 4), (5, 6) - Domain = 3, 5 Range: second coordinates in a set of ordered pairs, y values (3, 4), (5, 6) - Range = 4, 6 Function: Pairing between two sets of numbers in which each element of the first set is paired with exactly one element of the second set

3. Exercises: Determine the domain and range of each relation. 5. (2, 9), (3, 10), (5, 12), (9, 14) Domain: 2, 3, 5, 9 Range: 9, 10, 12, 14 7. (0, 17), (7, -12), (13, 21), (18, 40) Domain: 0, 7, 13, 18 Range: 17, -12, 21, 40 5. ( 2 , 9), ( 3 , 10), ( 5 , 12), ( 9 , 14) 5. (2, 9 ), (3, 10 ), (5, 12 ), (9, 14 )

4. Exercises: Determine whether each relation is a function 1. (12, 7), (6, 5), (12, -7), (6, -5) When two x values are the same, it is NOT a function. Domain: 12 and 12 Use the vertical line test to see if it is a function

5. Exercises: Determine whether each relation is a function 3. (1, 3), (2, 3), (4 ,3), (5 ,3) (6, 3) When two y values are the same, it IS a function. Range: 3 Use the vertical line test to see if it is a function

6. 5.1 Linear Functions and Graphs Practice Masters Level B

7. For each relation, (a) describe the domain, (b) describe the range, and (c), determine whether the relation is a function 1. (8, 12.5), (10, 12.3), (15, 12.1) a. Domain: 8, 10, 15 b. Range: 12.5, 12.3, 12.1 c. Function

8. Complete each ordered pair so that it is a solution to 2x - y = 10 (2, ___ ) (___, 8) (-1, ___)

9. The table below shows the cost for film developing. A processing fee of $2.00 is charged per roll, and there is an additional fee per picture. 9. Write an equation for the function. Every 3 pictures increases 30 cents Every 1 picture increases 10 cents $2.00 processing fee Y = 2 + 0.10x Number of pictures, x 12 15 24 36 Cost, in dollars, y $3.20 $3.50 $4.40 $5.60

10. 10. Write a set of ordered pairs for the function. (12, 3.20) (15, 3.50) (24, 4.40) (36, 5.60) Number of pictures, x 12 15 24 36 Cost, in dollars, y $3.20 $3.50 $4.40 $5.60

11. 11. Identify the domain shown in the table. 12, 15, 24, 36 Number of pictures, x 12 15 24 36 Cost, in dollars, y $3.20 $3.50 $4.40 $5.60

12. 12. Identify the range shown in the table. 3.20, 3.50, 4.40, 5.60 Number of pictures, x 12 15 24 36 Cost, in dollars, y $3.20 $3.50 $4.40 $5.60

13. 13. The graph below shows a linear function. Complete the table of values, and determine an equation of the line. Y = 2x + 1 X Y 0 1 2 3 X Y 0 1 1 3 2 5 3 7