Warm Up

1. In the ________________ , is the _______________ and is the ____________________.

2. Simplify .

3. Find the value of when :

4. Find the value of when :

5. Jenny has dollars in her savings account. If she deposits dollars in her savings

account each week, which expression represents the amount she will have in

her savings account at the end of a year?

Lesson 25: Differentiating Between Relations and

Functions

Functions

Vocabulary

• Domain: input values (x-values)

• Range: output values (y-values)

• Relation: set of ordered pairs where each number in the domain is matched to one or more numbers in the range

• Function: mathematical relationship where each value in the domain is mapped to exactly one value in the range

Example

Give the domain and range of the relation.

Example

Determine whether is a function.

Example

Determine whether represents a function.

Vertical Line Test

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

• Vertical line test: if a vertical line intersects a graph in exactly one point, then the graph represents a function.

Example

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

Functions

• In functions, the independent variable determines the value of the dependent variable. This means the dependent variable is a function of the independent variable . In terms of the variables, is a function of and can be written like the following example:

Example

a. Write in the form

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

Example

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.

Homework questions

• Questions on the homework?

Correcting Homework

• Be kind.

• Pay attention

• If the paper in front of you has 4 or more empty squares, return it to its owner.

• Write “C.B. ____________” with your name

Homework

• 1st and 2nd hour: Lesson 25 #1-30

• 3rd hour: Lesson 25 #1-15