This is a free lesson from our course in Algebra I
In this lesson, you'll learn what are functions and understand concepts such
as relation, notation, domain and range of a function. Some of the high level
definitions of these concepts are being mentioned below. They are as follows:
• a function is a relation between two sets of values, where the second value (the
"output") is uniquely determined by the first value (the "input").
(More text below video...)
(Continued from above)
• a relation is a collection of ordered pairs. If the pair has real numbers, e.g. (5, 2), then the relation may be graphed
on a pair of coordinate axis and they may satisfy a formula. For example,
Set A is all the people in a class and Set B is their height. The pairing of names
with corrosponding height is a relation.
• if every element of Set A has a unique image in a Set B, then it is a function.
E.g., y = f(x) = x^{2} + 2, means for every value
of x we get a unique value of f(x). If y is completely
determined by a quantity x, then y is the function of x,
denoted by f(x). For example, the area of a circle with radius r
is denoted by f(x) = r^{2}.
• domain is all the possible values of x and the range is all the resulting
possible values of y.
• a mapping, f: A —> B in which each element of set A is the
image of at least one element in set B.
We suggest you to go through the explanation provided in the video above by our instructor.
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