Determine whether each relation defines a function. See Example 1...

Question

Determine whether each relation defines a function. See Example 1.{(5, 1), (3, 2), (4, 9), (7, 8)}

Accepted Answer

Welcome back. I am so glad you're here. We are asked is the given relation, a function. And then we are given a set with four ordered pairs. The first ordered pair is 12 15. The second ordered pair is 1933. The third ordered pair is 27 14 and the fourth ordered pair is 39 51. Our answer choices are answer choice. A yes and answer choice. B no. All right. So what makes a relation a function? We recall from previous lessons for the definition of a function? For each distinct input? There is exactly one output. So what does that mean? Well, our input, that's going to be our X values, our output. That's going to be our Y values. But which ones are our X values? And which ones are our Y values in an ordered pair? The X values come first and the Y values come second. So our X values here are 12, 1927 and 39. Now, two things have to be true about the inputs about the X values first. They need to be distinct. What does that mean? It means they cannot repeat themselves. So, are these X values distinct 12, 1927 39. None of those repeat, they are distinct. Yes. Now, the other part of this is that for each distinct input, for each X value, there's exactly one output, exactly one Y value. And when these are listed as ordered pairs, there's is only going to be one output. Each X value only has that one Y value with it. So yes, this is a function. We look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one.

Determine whether each relation defines a function. See Example 1.{(5, 1), (3, 2), (4, 9), (7, 8)}

Key Concepts

Definition of a Function

Ordered Pairs

Vertical Line Test

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