Bell Quiz

Objectives

• Determine if a relation is a function.

Domain and Range

• The domain is the set of possible values for the independent variable (x-values or input values) of a set of ordered pairs.

• The range is the set of values for the dependent variable (y-values or output values) of a set of ordered pairs.

Relation

• A relation is a set of ordered pairs where each number in the domain (x) is matched to one or more numbers in the range (y).

• Relations can also be represented using:– Set notation– Tables– Diagrams– Equations.

Example 1Determining the Domain and Range of a Relation

Give the domain and range of the relation.

{(2, 6), (2, 10), (8, 6), (5, 1), (4, 6), (3, 9)}

Domain:

Range:

Lesson Practice

Give the domain and range of the relation.

{(1, 2), (2, 1), (4, 6), (8, 5), (7, 7), (3, 10)}

Domain:

Range:

Functions

• A function is a mathematical relationship pairing each value in the domain with exactly one value in the range.

• The domain (or x-value) can not be paired with more than on y-value.

Example 2Identifying a Set of Ordered Pairs as a Function

Determine whether the set represents a function.

{(3, 3), (10, 1), (0, 3), (8, 9), (4, 4), (10, 2)}

Example 3Identifying a Set of Ordered Pairs as a Function

Determine whether the set represents a function.

Lesson Practice

Determine whether the set represents a function.

{(11, 12), (12, 1), (5, 5), (14, 10), (13, 7)}

Lesson Practice

Determine whether y = 3x – 1 represents a function.

Vertical-Line Test

• If a relation is graphed on a coordinate grid, the vertical-line test can be used to determine if the relation is a function.

Example 4Identifying a Graph as a Function

Use the table. Graph the ordered pairs on a coordinate grid and determine whether the ordered pairs represent a function.

Lesson Practice

Use the table. Graph the ordered pairs on a coordinate grid and determine whether the ordered pairs represent a function.

Functions

• In a function, the independent variable determines the value of the dependent variable.

• This means the dependent variable y is a function of the independent variable x.

• In terms of the variables, y is a function of x and can be written like the following example:

y = f(x)

y = 6x + 3

f(x) = 6x + 3

Example 5Writing a Function

Write x + 2y = 5 in function form

Example 6Writing a Function

Food labels list the grams of fats, carbohydrates, and proteins in a single serving. Proteins covert to 4 calories per gram. Write a rule in function notation to represent the number of calories from protein.

Lesson Practice

A brochure costs $0.07 per page to print. Write a rule in function notation to represent the cost of printing c copies of the brochure.

Example 7Application: Reading

A student reads an average of 25 pages per day while reading a 544 page novel. Write a rule in function notation to find the number of pages she has left to read at the end of any given day.

Lesson Practice

An author writes 30 pages per day. Write a function rule that the author can use to find how many pages she has left to write before reaching page 400.