CHAPTER 2: FUNCTIONS, EQUATIONS, AND GRAPHS2.1 Relations and Graphs

RELATIONS A relation is a set of pairs of input and output

values. There are four ways to represent relations

EXAMPLE: REPRESENTING RELATIONS The monthly average water temperature of

the Gulf of Mexico in Key West, Florida varies during the year. In January, the average water temperature is 69°F, in February, 70°F, in March, 75°F and in April, 78°F. How can you represent this relation in four different ways?

DEFINITIONS

The domain of a relation is the set of inputs, also called the x-coordinates, of the ordered pairs.

The range is the set of outputs, also called the y-coordinates, of the ordered pairs.

EXAMPLE: FIND THE DOMAIN AND RANGE OF EACH.

FUNCTIONS A function is a relation in which each

element of the domain corresponds to exactly one element of the range. When using a mapping diagram to represent a

relation, a function has only one arrow from each element of the domain. Example:

EXAMPLE: IS THE RELATION A FUNCTION?

THE VERTICAL LINE TEST

The vertical line test is used to test whether a graph represents a function.

The vertical line test states that if any vertical line passes through more than one point on the graph of a relation, then the relation is not a function.

EXAMPLE: USE THE VERTICAL LINE TEST. WHICH GRAPH(S) REPRESENTS A FUNCTION?

FUNCTIONS A function rule is an equation that

represents an output value in terms of an input value. We write a function rule in function notation.

EXAMPLE: USING FUNCTION NOTATION For , what is the output for

the inputs:

2 5f x x

13,0,&

4

EXAMPLE: USING FUNCTION NOTATION For ,what is the output

for

the inputs:

4 1f x x

2,0,5

EXAMPLE: Tickets to a concert are available online for $35

each plus a handling fee of $2.50. The total cost is a function of the number of tickets bought. What function rule models the cost of the concert tickets? Evaluate the function for 4 tickets.

EXAMPLE

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