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

Question

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

x y
 3 -4
 7 -4
10 -4

Accepted Answer

Welcome back. I am so glad you're here. We are asked is the given relation, a function and we're given an XY table. The first column is the X values. The second column is the Y values underneath X and Y. There are three rows. The first row has an X value of 15 and A Y value of negative 12. The second row has an X value of 22 and A Y value of negative 12. The third row has an X value of 36 and A Y value of negative 12. Our answer choices are answer choice. A yes and answer choice. B no. All right. So what makes something a function we recall from previous lessons for the definition of a function for each distinct input? There is exactly one output. So what are the parts of our relation here? Well, input, that's going to be our X values and output. That's going to be our Y values. So a couple of things have to be true about our X values first. They need to be distinct. What does that mean? It means that the X values cannot repeat themselves. So do they repeat themselves? Here. 15, 22 and 36. Nope, none of those are repeats. So cool, we've got the distinct input part down. Now, the other part is that for each distinct input, there can be exactly one output. In other words, for each X value, it can't have multiple Y values listed. So do each of these distinct inputs have exactly one output. Yes, 15 only has negative 12, 22 only has negative 12, 36 only has negative 12. So yes, we do have a function here. Now, you might have noticed that our outputs do repeat themselves here. They're all negative 12. But that's totally fine. The Y values the outputs, they can do whatever they want, they can repeat themselves as much as they want. It's just the X values that cannot. So we do have a function that 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. x y 3 -4 7 -4 10 -4

Key Concepts

Definition of a Function

Mapping of Inputs to Outputs

Vertical Line Test

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