2-1: Relations and Functions

Definitions:

Relation: is any set of pairs of input and output values. Usually the input values are represented by x, and the output values are represented by y.

Function: is a relation in which each element of the input list corresponds to exactly one element of the output list.

Domain: the set of all the input elements. (x items)

Range: the set of all the output elements. (y items)

Vertical Line Test: if any vertical line drawn passes through more than one point on the graph, then the relation is not a function.

Independent variable: is the x or input variable.

Dependent variable: is the y ( f(x) ) or output variable.

Four ways to represent a relation

(1) Ordered pairs (x, y)(2) Mapping diagram(3) Table of values (T-Chart)(4) Graph placed on a coordinate plane

* Look at page 64 in textbook for examples of each!!

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Example 1: Skydiving: When skydivers jump out of an airplane they experience free fall. The photos show various heights of a skydiver at different times during free fall, ignoring air resistance.

a.) How can you represent this relation?

b.) What is the domain of this relation? What is the range?

c.) Is the skydiving relation a function? Explain.

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Example 2: What are the domain and range of each relation?

A. B. {(0, 1), (1, 2), (3, 5), (4, 8), (6, 9)}

C. D.

x y-2 4-1 10 01 12 4

Example 3: Is each relation a function?

A. B. {(0, 1), (1, 2), (3, 5), (4, 8), (6, 9)}

C. D.

x y-2 4-1 10 01 12 4

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Key Question: Does the equation y = 3x + 2 represent a function?

If an equation represents a function, you can write it in function notation, where you replace the y with f(x).

Example 4: If f ( x )=3 x−42 , find the following outputs:

a.) f(2) b.) f(-4) c.) f(0)

If f ( x )=−2x+5, find the following outputs if:

d.) f(-3) e.) f(0) f.) f ( 14 )

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Example 5: Tickets to a concert are available online at a cost of $35 per ticket, plus an online processing fee of $5.00. The total cost is a function of the number of tickets bought. Write a function rule to model the total cost of the concert tickets, then evaluate the function for 4 tickets.

You Try:

a.) Write a function rule to model the cost of an electric bill.

b.) Evaluate the function if you use 500 kilowatts in a billing period.

Homework: pp. 68 – 69 => 2; 4; 10 – 22 even pp. 71 – 72 => 8 – 16; 19 - 25

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Electric Company Costs

$40 base fee for service$0.15 charge per kilowatt used