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Amsco Integrated Algebra I: Sets, Relations, and Functions |
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This is a free lesson from our course in Amsco's Integrated Algebra
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This lesson explains the concepts of sets, relations, functions and how to represent
them. You’ll recall from the earlier learning use of the roster form and set builder
notation to describe sets. In roster form, the elements of a set are enclosed by
braces and listed once and repeated elements are not allowed. Set-builder notation
is a mathematically concise way of describing a set without listing the elements
of the set. The symbol for set is { }. E.g.
Set of integers in roster form: {. .
., -3, -2, -1, 0, 1, 2, 3, . . .}
Set-builder notation, for the set counting from
1 to 100: {x| x is a whole number and 1 ≤ x ≤ 100}. A relation is a set of ordered
pairs. E.g. {(0, 1), (5, 2), (-3, 9) }.
(More text below video...)
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(Continued from above)
You’ll build skills in this lesson through manipulating relations as graphs, tables
and ordered pairs. Then will have explanation of relations that are finite sets
and infinite sets. To represent a relation as a set of ordered pairs, it is necessary
to write each set of associated values in parentheses and separated by a comma.
Each ordered pair should be written with the x-value first, and then the y-value.
The normal way of representing a relation is to express a relation, as a plot of
points on a coordinate plane. You’ll first draw a coordinate plane, then plot each
set of associated values at the corresponding point on the plane, followed by x
number of steps horizontally from the origin, and y steps vertically. When construct
as a table, list each set of associated values side-by-side in a two-column table,
under the appropriate column heading; either x or y.
The domain of a relation is
the set of all first elements of the ordered pairs and the range of a relation is
the set of all second elements of the ordered pairs. E.g. the domain and range of
a relation, {(0, 4), (8, 15), (70, 33)} are:
Domain: 0 8 70
Range: 4 15 33
A function
is a relation in which every element of the domain is paired with one and only one
element of the range i.e. in which the member of the domain (x- values) don’t repeat.
Here for every x- values, there is only one y- value.
Relation 1- {(0, 4), (4, 8),
(8, 16)}, has one y value for each x value: It is a function.
Relation 2- {(0, 4),
(4, 8), (4, 16)}, has different y values i.e. 8 and 16 for the same x value of 4.
Thus it is not a function.
Remember:
Relation: a set of ordered pairs
Domain: the
set of all first elements of the ordered pairs (x-coordinates)
Range: a set of all
second elements of the ordered pairs of the function (y-coordinates)
In cases of
domain and range, don’t repeat the values.
Symbolic representation to indicate that
an element is a member of a set is , and the symbol means that an element is not
a member of a set.
The video above explains in detail and offers math home work help solving several examples of sets, relations, functions and how to represent them.
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