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SVETLANKA909090 [29]
3 years ago
11

Hey plsss help meeeeee

Mathematics
1 answer:
nalin [4]3 years ago
7 0

Answer:

The first, third, and fourth answer choices represent a function.

Step-by-step explanation:

A relation is a relationship between sets of values. The two quantities that are being related to each other are the input (x-variable) and the output (y-variable). But relations in general aren't always a good way to relate between x and y.

Say that I have situation where I want to give <em>x </em>dollars to the cashier so he can change them to <em>y</em> quarters. Here is a "example" of the relation:

Dollars (x) | Quarters (y)            

----------------------------------              

       0       |          0                      

        1       |          4                      

       2       |          8

       2       |          12

Do you see something wrong here? Yes! We all know that you can't exchange 2 dollars for 12 quarters. You can only exchange 2 dollars for 8 quarters and only 8 quarters. This is a general reason why we don't rely on general relations for real-life situations. One x-variable does not exactly map to one and only one y-variable.

However, a relation that can map one x-variable to one and only one y-variable is known as a function. Let's make the above example an actual function to prove a point:

Dollars (x) | Quarters (y)            

----------------------------------              

       0       |          0                      

        1       |          4                      

       2       |          8

       3       |          12

Now, the 3 dollars make 12 quarters as it should. This is how a function should look like.

There are two ways to check if a relation is a function. On a relation, table, or a set of ordered pairs, you have to make sure there is no "x-variable" that repeats. All x-values of a relation have to be unique in order to be a function. On a graph, you can also perform the Vertical Line Test. If you draw vertical lines over a relation and if the lines cross only once, then it is a function. If not, it fails the Vertical Line Test.

So to answer you're question, the first, third, and fourth choices are functions because they all have unique x-variables. The second choice is not a function because it fails the Vertical Line Test.

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