Domain, Range and

Functions.

Introduction

Algebra I

The relationship between sets of information from with a set of starting points called domain and ending points called range.

Relation

RelationDomain

xRange

y

0 1

1 2

2 3

3 4

4 5

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

Domain

Domain

0

1

2

3

4

x y

0 1

1 2

2 3

3 4

4 5

The x-values of the ordered pairs.

Range

Range

1

2

3

4

5

x y

0 1

1 2

2 3

3 4

4 5

The y-values of the ordered pairs.

1. What the is domain?{(2, –3), (4, 6), (3, –1), (6, 6),

(2, 3)} A. {-3,6,-1,6,3}

D. {-3,-1,3,6}

B. {2,4,3,6,2}

C. {2,3,4,6}

2. Write the domain as a set.

(4,3) (-1,4) (6,7)(5,2) (-2,1) (3,9) A. {4,-1,6,5,-

2,3} B. {-2,-1,3,4,5,6} C. {1,2,3,4,7,9} D. {-2,-1,2,3,4,5}

3.With the relation, the y-values are considered

A. Range

B. Ending points C. Starting points D. A and B

C. {(3,9),(5,8),(-9,1),(-2,4),(5,-2)}

B. {(5,2),(1,1),(-2,3),(-9,1),(4,4)}

4. What is the relation with the

corresponding range?{-9,-2,1,4,5} A. {(1,5),(3,1),(1,-2),(4,-9),

(1,4)}

D. {(5,3),(-2,4),(1,1),(-9,1),(4,4)}

5.When looking for the domain,

you are really looking for the

y-values of the relation. A. True

B. False

6. What is the range?{(-1,2),(3,2)}

A. {-1,3}

B. {2}

Function

This is considered a“well-behaved” relation.

Function

If you find a duplicate x-value, then you do not have a function

FunctionDomai

nRange

0 1

1 2

2 3

3 4

4 5Domai

nRange

306

138

2 1

These are functions. There are only one x for every y, even if there are is two x’s for one y. Focus on the x’s.

FunctionDomai

nRange

0 1

1 2

2 3

3 4

4 5

These are not functions. Two x’s for one y. Unacceptable.An x without even a y? Very unacceptable.

Domain

Range

7 9

4 0

0 3

1 4

2

Graph Try Vertical Line Test.

To be a function or to not be?

Graph What do you think?

To be a function or to not be?

7. For a relation to be a function, you cannot

A. have duplicate x-values. B. have duplicate y-values.

8. Is this a function?(4,3) (-1,4) (6,7)(5,2) (-2,1) (3,9)

A. No

B. Yes

9. Why is this a function?(4,3) (-1,4) (6,2)(5,2) (-2,1) (3,9)

A. {1,2,3,4,9}

B. {-2,-1,3,4,5,6} C. {-2,1,3,4,5,6} D. A and B.