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A set of ordered pairs is called a __________. A set of ordered pairs is called a relation . A ________ is a set of ordered pairs in which no two ordered pairs have the same first coordinate and different second coordinates.
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A ________ is a set of ordered pairs in which no two ordered pairs have the same first coordinate and different second coordinates.
A function is a set of ordered pairs in which no two ordered pairs have the same first coordinate and different second coordinates.
The ________ of a function is the set of all the _____ coordinates of the ordered pairs.
The domain of a function is the set of all thefirst (x) coordinates of the ordered pairs.
The ________ of a function is the set of all the ______ coordinates.
Therange of a function is the set of all the second (y) coordinates.
Functional Notation f ( x)
Vertical Line Test for Functions • A graph is the graph of a function if and only if no vertical line intersects the graph at more than one point.
Increasing, Decreasing and Constant Functions If a and b are elements of an interval I that is a subset of the domain of a function f, then
Increasing, Decreasing and Constant Functions If a and b are elements of an interval I that is a subset of the domain of a function f, then • f is increasing on I if f(a) < f(b) whenever a < b.
Increasing, Decreasing and Constant Functions If a and b are elements of an interval I that is a subset of the domain of a function f, then • f is increasing on I if f(a) < f(b) whenever a < b. • f is decreasing on I is f(a) > f(b) whenever a > b.
Increasing, Decreasing and Constant Functions If a and b are elements of an interval I that is a subset of the domain of a function f, then • f is increasing on I if f(a) < f(b) whenever a < b. • f is decreasing on I is f(a) > f(b) whenever a > b. • f is constant on I if f(a) = f(b) for all a and b.
Horizontal Line Test • If every horizontal line intersects the graph of a function at most once, then the graph is the graph of a one to one function.
Functions whose graphs can be drawn without lifting the pencil off the paper are called continuous functions.