is 3 3 a function Step by Step Examples Algebra Relations Determine if the Relation is a Function 5 9 5 9 3 0 3 0 Since there is one value of y y for every value of x x in 5 9 3 0 5 9 3
The point 1 5 shows up twice while the point 3 8 is written three times This table can be cleaned up by writing a single copy of the repeating ordered pairs The relation is now clearly a function Functions and relations are subsets of the cartesian product of two sets For example if A 1 2 3 and B a b c are two sets then R 1 a 1 b 2 c is a relation F 1 b 2 a 3 c is a function How to Identify
is 3 3 a function
is 3 3 a function
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One of the core concepts in College Algebra is the function There are many ways to describe a function and we begin by defining a function as a special kind of relation Since each person has exactly one birthday the relation in Example 3 43 is a function The relation shown by the graph in Example 3 44 includes the ordered pairs 3 1 3 1 and 3 4 3 4 Is that okay in a function No as
A function is a relation where each input has exactly one output Function notation looks like f input output or f x y We use this notation to define the rule of the function through an equation based on x What is a function In mathematics a function can be defined as a rule that relates every element in one set called the domain to exactly one element in another set called the range
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Definition Function Let A and B be nonempty sets A function from A to B is a rule that assigns to every element of A a unique element in B We call A the domain and B the codomain of the No it is not a function A function is a relation a set of ordered pairs with the additional property that no two pairs have the same first element and different second
Relation 1 and Relation 3 are functions because each x value each element in the domain has one and only only one y value or one and only number in the range Remember if a domain The simplest definition is a function is a bunch of ordered pairs of things in our case the things will be numbers but they can be otherwise with the property that the first members of the
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is 3 3 a function - State the domain and range for the elements matched in the diagram below State whether the matches form a function Solution Domain 3 4 5 6 7 Range 1 2 9 12 Note that the