Prentice Hall Algebra 2

Chapter 2 Functions, Equations, and Graphs > 2-1 Relations and Functions

To model a real-world situation using a function rule, you need to identify the dependent and independent quantities. One way to describe the dependence of a variable quantity is to use a phrase such as, “distance is a function of time.” This means that distance depends on time.

Problem 6 Writing and Evaluating a Function

Ticket Price 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.

Cost is the dependent quantity and the number of tickets is the independent quantity.

Relate	begin box , cap total cost , end box	is	begin box , cost per ticket , end box	times	begin box , number of tickets bought , end box	plus	begin box , handling fee , end box
Define	Let begin box , t , end box = number of tickets bought. Let begin box , c open t close , end box = the total cost.
Write	begin box , t , end box = number of tickets bought. Let begin box , c open t close , end box	=	begin box , 35 , end box	·	begin box , t , end box	+	begin box , 2.50 , end box

C ( t ) = 35 t + 2.50 C ( 4 ) = 35 · 4 + 2.50 Substitute 4 for t . = 142.50 Simplify. table with 3 rows and 3 columns , row1 column 1 , c open t close , column 2 equals 35 t plus , 2.50 , column 3 , row2 column 1 , c open 4 close , column 2 equals 35 middle dot 4 plus , 2.50 , column 3 cap substitute . 4 , for , t . , row3 column 1 , , column 2 equals , 142.50 , column 3 cap simplify. , end table

The cost of 4 tickets is $142.50.

✓ Got It?

You are buying bottles of a sports drink 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.

✓ Lesson Check

Do you know HOW?

List the domain and range of each relation.

{ open 3 comma negative 2 close comma (4, 4), open 0 comma negative 2 close comma (4, 1), (3, 2)}
{(0, 4), (4, 0), ( negative 3 comma negative 4 ), ( negative 4 comma negative 3 )}

Determine whether each relation is a function.

{ open 3 comma negative 8 close comma ( negative 9 comma 1 close comma (3, 2), ( negative 4 comma 1 close comma ( negative 11 comma negative 2 )}
{(1, 1), (2, 0), (3, 1), (4, 3), (0, 2)}

Do you UNDERSTAND?

Vocabulary Can you have a relation that is not a function? Can you have a function that is not a relation? Explain.
Error Analysis Your friend writes, “In a function, every vertical line must intersect the graph in exactly one point.” Explain your friend's error and rewrite the statement so that it is correct.
Reasoning Why is there no horizontal-line test for functions?

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Problem 6 Writing and Evaluating a Function

Think

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✓ Lesson Check

Do you know HOW?

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