Relations and Functions: Basics. A. Relations. 1. A relation is a set of ordered pairs. For example,. A = {(-1,3), (2,0), (2,5), (-3,2)}. 2. Domain is the set of all. in class by Adam Osborne: namely, we can think of a relation R as a function from drawback: it makes the definition of a relation depend on that of a function. Sets, Relations and Functions. After studying this lesson, you will be able to: ○ define a set and represent the same in different forms;. ○ define different types.

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The set of all first elements in a relation R, is called the domain of the relation R Functions A relation f from a set A to a set B is said to be. PDF | A relation is used to describe certain properties of things. That way, certain things be connected in some way; this is called a relation. Contents. 1. Relations. 1. The idea of a relation. 1. The formal definition of a relation. 2. Basic terminology and further examples. 2.

One reason is that 2 is the first element in more than one ordered pair, 2, B and 2, C , of this set. Two other reasons, also sufficient by themselves, is that neither 3 nor 4 are first elements input of any ordered pair therein. Intuitively, a function is a process that associates to each element of a set X a single element of a set Y. The set G is called the graph of the function. Formally speaking, it may be identified with the function, but this hides the usual interpretation of a function as a process.

So let's think about its domain, and let's think about its range. So the domain here, the possible, you can view them as x values or inputs, into this thing that could be a function, that's definitely a relation, you could have a negative 3. You could have a negative 2.

You could have a 0. You could have a, well, we already listed a negative 2, so that's right over there. Or you could have a positive 3. Those are the possible values that this relation is defined for, that you could input into this relation and figure out what it outputs.

Now the range here, these are the possible outputs or the numbers that are associated with the numbers in the domain. The range includes 2, 4, 5, 2, 4, 5, 6, 6, and 8.

I could have drawn this with a big cloud like this, and I could have done this with a cloud like this, but here we're showing the exact numbers in the domain and the range.

And now let's draw the actual associations. So negative 3 is associated with 2, or it's mapped to 2.

So negative 3 maps to 2 based on this ordered pair right over there. Then we have negative 2 is associated with 4.

So negative 2 is associated with 4 based on this ordered pair right over there. Actually that first ordered pair, let me-- that first ordered pair, I don't want to get you confused. It should just be this ordered pair right over here. Negative 3 is associated with 2. Then we have negative we'll do that in a different color-- we have negative 2 is associated with 4. Negative 2 is associated with 4.

We have 0 is associated with 5. Or sometimes people say, it's mapped to 5. We have negative 2 is mapped to 6. Now this is interesting. Negative 2 is already mapped to something.

Now this ordered pair is saying it's also mapped to 6. And then finally-- I'll do this in a color that I haven't used yet, although I've used almost all of them-- we have 3 is mapped to 8. So the question here, is this a function? And for it to be a function for any member of the domain, you have to know what it's going to map to.

A relation is a set of one or more ordered pairs. In this case. A function maps each domain element to only one range element. Use the vertical line test to determine if the graphs represent a function.

The Vertical Line Test: Given the graph of a relation. The only graph given that passes the vertical line test is Y. The t-table Y is the only table that does not show a domain element paired with two or more range elements.

The graph does not pass the vertical line test. The Vertical-Line Test: A Explanations 1. The relation diagram where each input value has exactly one arrow drawn to an output value will represent a function.

For a relation to be a function. The only graph given that passes the vertical line test is Z. In the table below. The only mapping that does not map a domain element to two or more range elements is Z.

Z is not a function.

If the relation being tested is a vertical line. Since the graph does not pass the vertical line test.

A function maps each domain element to only one range element. The t-table Y is the only table that does not show a domain element paired with two or more range elements.

A function is a set of ordered pairs such that for each domain element there is only one range element. In this case, there is one y-coordinate for every x-coordinate. The vertical line test can be used to determine this. Therefore, it is both a relation and a function.

The Vertical-Line Test: Given the graph of a relation, if a vertical line can be drawn that does not cross the graph in more than one place, it is a function.

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