Algebra IIRelations and Functions

VOCABULARY

1. For every input of a function there is exactly/at least/at most one output.

VOCABULARY

Relation (noun) ree LAY shunRelated words: input, output, domain, range, function

Definition: A relation is a set of ordered pairs of input and output values.

Examples: {(0,1),(2,3),(0,4)}

RELATION

{(0,1), (2,3), (0,4)}

Input (domain)

Output (range)

Circle the output values in the relation.

{(1,0), (-2,3), (3,2), (5, -4)}

Write the domain of the relation.

{(-2,3), (-2,1), (5, 4)}

{−2,5 }

There are 4 different ways to represent a relation:

Mapping diagramOrdered pairsTableGraph

Representing a Relation

The average water temperature of the Gulf of Mexico in Key West, Florida varies during the year. In January, the average water temperature is F; in February, F; in March F; and in April, F. How can you represent this relation in four different ways?

Mapping DiagramThe average water temperature of the Gulf of Mexico in Key West, Florida varies during the year. In January, the average water temperature is F; in February, F; in March F; and in April, F. How can you represent this relation in four different ways?

Jan.

Feb.

Mar.

Apr.

69

____

____

____

707578

Ordered pairsThe average water temperature of the Gulf of Mexico in Key West, Florida varies during the year. In January, the average water temperature is F; in February, F; in March F; and in April, F. How can you represent this relation in four different ways?

{(Jan., 69), (Feb, ___), (Mar., ___), (Apr., ___)}

70

75

78

TableThe average water temperature of the Gulf of Mexico in Key West, Florida varies during the year. In January, the average water temperature is F; in February, F; in March F; and in April, F. How can you represent this relation in four different ways?

x (Month) y ()Jan. 69

Feb.Mar.Apr.

707578

GraphThe average water temperature of the Gulf of Mexico in Key West, Florida varies during the year. In January, the average water temperature is F; in February, F; in March F; and in April, F. How can you represent this relation in four different ways?

64

66

68

70

72

74

76

78

80

Month

Tem

pera

ture

(

) 𝒐𝑭

JAN.

FEB.

MAR.

APR.

What is the domain and range of this relation?

{(-3, 14), (0, 7), (2, 0), (9, -18), (23, -99)}

Domain: {-3, 0, 2, 9, 23}

Range: {-99, -18, 0, 7, 14}

First the set of x- coordinates:

Then the set of y- coordinates:

The set of x-coordinates is the ________ of the relation.

domain

The set of y-coordinates is the ________ of the relation.

range

Identifying Functions

Circle the range values that correspond to domain value 2.

Domain

Range

2346

-3-136 -3 -1 3

6

True or False?Every element of the input corresponds to exactly one element of the range.

TRUE

True or False?

The relation is a function.

FALSE

Domain

Range

2346

-3-136

Vertical line testA relation is a function if it can pass the vertical line test. Which means when the relation is on a graph you can not draw a straight vertical line and touch more than one point.

NO

NO

YES!!

Use the vertical line test. Which graph(s) represent(s) a function?

NO YES YES

Underline the correct word(s) to complete the sentence.

If a vertical line passes through more than one point on a graph, the graph represents/does not represent a function.

Function Notation

For , what is ?

Circle the given input.

Substitute the input into the function rule and simplify:

;

−2 −2+8+1¿9

Writing and Evaluating a Function

You are buying bottles of a sports drink mix for a softball team. Each bottle costs $1.19. What function rule models the total cost of a purchase? Evaluate the function for 15 bottles.

Writing and Evaluating a FunctionYou are buying bottles of a sports drink mix for a softball team. Each bottle costs $1.19. What function rule models the total cost of a purchase? Evaluate the function for 15 bottles.

Let c = ?. Circle your choice.

cost per bottle cost of 15 bottles number of bottles bought total cost

Writing and Evaluating a FunctionYou are buying bottles of a sports drink mix for a softball team. Each bottle costs $1.19. What function rule models the total cost of a purchase? Evaluate the function for 15 bottles.

Then Circle your choice.

cost per bottle cost of 15 bottles number of bottles bought total cost

Writing and Evaluating a FunctionYou are buying bottles of a sports drink mix for a softball team. Each bottle costs $1.19. What function rule models the total cost of a purchase? Evaluate the function for 15 bottles.

Relate:

TOTAL COST is COST PER BOTTLE times NUMBER OF BOTTLESBOUGHTWrite:

* _______c 1.19 c

Writing and Evaluating a FunctionYou are buying bottles of a sports drink mix for a softball team. Each bottle costs $1.19. What function rule models the total cost of a purchase? Evaluate the function for 15 bottles.Evaluate at 15 bottles:

So it will cost $17.85 for 15 bottles.

Lesson Check

Error Analysis:

Your friend writes, “In a function, every vertical line must intersect the graph in exactly one point.” Explain your best friends error and rewrite his statement so that it is correct.

Lesson CheckDraw a vertical line on each graph that does not intersect the function.

Lesson Check

Error Analysis:

Your friend writes, “In a function, every vertical line must intersect the graph in exactly one point.” Explain your best friends error and rewrite his statement so that it is correct.

In a function, a vertical line must intersect the graph in exactly one point.

Math SuccessCheck off the vocabulary words you understand.

□relation □function □domain□range

Rate how well you can represent and interpret functions.

0 2 4 6 8 10NEED TO REVIEW

NOW I GET IT!