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This is your introduction to domain, range, and functions. You will learn more about domain, range, functions, relations, x-values, and y-values. There are definitions and explanations of each concepts. There are questions to help quiz yourself. Test your abilities. Enjoy.
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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.
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