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High School Mathematics - 2
4.11 Functions, Relations, Domain & Range

Relation: A relation is simply a set of ordered pairs.

The first elements in the ordered pairs, the x-values, form the domain. The second elements in the ordered pairs, the y-values, form the range.


This mapping shows a relation from set A into set B. The relation consists of the ordered pairs (1,2), (1,3), (4,6), (5,6), and (7,8).
The domain is the set {1, 4, 5, 7}
The range is the set {2, 3, 6, 8}.
The range is the dependent variable.

Function:
A function is a set of ordered pairs in which each element of the domain has only ONE element associated with it in the range.

The relation shown above is NOT a function because the element 1 (in the domain) is mapped to two elements in the range, 2 and 3.

A function may have two x-values assigned to the same y-value, but may not have two y-values assigned to the same x-value.

Example

Domain = {1,4,5,7}
Range = {2,3,6,8}
Relation = {(1,2), (4,3), (5,6), (7,8)}
This relation is a function.


Directions: Answer the following. Enclose the answer in curly brackets { }. Also write at least 5 examples of your own.
Q 1: The domain of the function y = 2x is 0,2,5,7, and 8. Find the range of the function.
Answer:

Q 2: State the range of the following relation. {(3, 5), (2, 5), (1, 5), (0, 5), (1, 5), (2, 5)}
Answer:

Q 3: State the domain of the following relation: {(2, 3), (4, 6), (3, 1), (6, 6), (2, 3)}
Answer:

Q 4: Find the range of the function y = x - 5 given the domain {1,2,3,4}
Answer:

Q 5: Is the relation a function? {(2, 3), (4, 6), (3, 1), (6, 6), (2, 3)}
Function
Not a function

Q 6: Write the rule of the function:
Input014610
Output236812

y = x + 2
y = 2x + 1
y = 2x

Q 7: State the range of the following relation: {(2, 3), (4, 6), (3, 1), (6, 6), (2, 3)}
Answer:

Q 8: The domain of the function y = x + 3 is 0,1,2,3, and 4. Find the range.
Answer:

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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