5.1 Linear Functions and Graphs

Student Study Guide

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

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)

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

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

5.1 Linear Functions and Graphs

Practice Masters Level B

For each relation, (a) describe the domain, (b) describe the

range, and (c), determine whether the relation is a

function1. (8, 12.5), (10, 12.3), (15, 12.1)

a. Domain: 8, 10, 15

b. Range: 12.5, 12.3, 12.1

c. Function

Complete each ordered pair so that it is a solution to 2x - y =

10

3. (2, ___ )4. (___, 8)5. (-1, ___)

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

Number of pictures, x

12 15 24 36

Cost, in dollars, y

$3.20 $3.50 $4.40 $5.60

Every 1 picture increases 10 cents

$2.00 processing fee

Y = 2 + 0.10x

10. Write a set of ordered pairs for the function.

(12, 3.20)

Number of pictures, x

12 15 24 36

Cost, in dollars, y

$3.20 $3.50 $4.40 $5.60

(15, 3.50)

(24, 4.40)

(36, 5.60)

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. 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. 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