4.6 Formalizing Relations and Functions:

Domain: The x value of the ordered pair (x, y)

Relation: the pairing of numbers in one set mainly the domain with exactly one number of the range represented by ordered pairs (x, y)

Range: The y value of the ordered pair (x, y)

Vertical Line Test: If any vertical line passes through a graph more than once it is a relations but not a function.

Function: Only hit the graph once

Not a Function: Hit the graph more than once

Graphs:

In math we use a few ways to identify a function:

1. Mapping Diagrams: The use of oval shapes to connect a number of the domain with the number of the range.

EX: Identify the domain and range using a mapping diagram then decide if the relation

is a function?

A: {(-2, 0.5), (0, 2.5), (4, 6.5), (5, 2.5)}

B: {(6, 5), (4, 3), (6, 4), (5, 8)}

A: {(-2, 0.5), (0, 2.5), (4, 6.5), (5, 2.5)}

Domain(x): {-2, 0, 4, 5}

Range(y):{0.5, 2.5, 6.5}

-2 0 4 5

0.52.56.5

The relation is a FUNCTION since there is only one y for each x.

B: {(6, 5), (4, 3), (6, 4), (5, 8)}

Domain(x):{4, 5, 6}

Range(y):{3, 4, 5, 8}

4 5 6

3 4 5

The relation is a NOT A FUNCTION since the six (x) has two (y) values: 4 and 5.

8

YOU TRY IT:

EX: Identify the domain and range using a mapping then decide if the relation a

function?

A: {(4.2, 1.5), (5, 2.2), (7, 4.8), (4.2, 0)}

B: {(-1, 1), (-2, 2), (4, -4), (7, -7)}

A: {(4.2, 1.5), (5, 2.2), (7, 4.8), (4.2, 0)}

Domain(x): {4.2, 5, 7}

Range(y):{0, 1.5, 2.2, 4.8}

4.2 5 7

01.52.2

The relation is a NOT A FUNCTION since there is two y’s for 4.2 .

4.8

A: {(-1, 1), (-2, 2), (4, -4), (7, -7)}

Domain(x): {-2, -1, 4, 7}

Range(y):{-7, -4, 1, 2}

-2 -1 4

-7-4 1

The relation is a FUNCTION since there is exactly one y for each x .

2 7

IDENTIFYING FUNCTIONS: A relation is a function if it passes the vertical line test.

1. Decide if the relation is a function.2. Provide domain and Range of the graph

A B C

D E

A relation is a function if it passes the vertical line test. A: Relation that is a function

B: Relation that is Not a function

C: Relation not Function

A relation is a function if it passes the vertical line test.

D: Relation that is a function

E: Relation that is Not a function since 3 has two y values.

DOMAIN : x values of our graph:RANGE: y values of our graph

D: { x | -∞< x < ∞}

R: { y |0 < y < ∞}

D: { x | 0 < x < ∞}

R: { y | - ∞ < y < ∞}

D: { x | -7 < x < 7}

R: { y |-2 < y < 2}

DOMAIN : x values of our graph:RANGE: y values of our graph

D: { x | -∞< x < ∞} R: { y | - ∞ < y < ∞}

D: { 1, 2, 3}

R: { a, b, c, d}

EVALUATION FUNTIONS: We evaluate a function by plugging in a given value of x.

1. Evaluate f(4)

A B

C E A person can type at a speed of w(x) = 250x. How many words will it be in 8 minutes?

EVALUATION FUNTIONS: We evaluate a function by plugging in a given value of x.

1. Evaluate f(4)

Looking at the value of x = 4, we see that the values of y are: - 2, and + 2

Looking at x = 4, we see that the values of y are about: - 1.8, and + 1.8

EVALUATION FUNTIONS: We evaluate a function by plugging in a given value of x.

1. Evaluate f(4)

A person can type at a speed of W(x) = 250x. How many words will it be in 8 minutes?

Looking at the value of x = 4, we see that the value of y will be 64, not in the graph.

We need to replace x for 8.W(x) =250xW(8) = 250(8) W(8) = 2000 words/minute

Y = x3

YOU TRY IT:

Provide the domain and range of the following:

YOU TRY IT (Solution):

Domain: {x | < x < }

RANGE: { y | -2 < y < 2}

CLASSWORK:

Page 271-273

Problems: As many as needed to master the

concept.