Determine whether each relation defines a function, and give the ...

Question

Determine whether each relation defines a function, and give the domain and range. See Examples 1 – 4.

x y
 0 0
-1 1
-2 2

Accepted Answer

Welcome back. I am so glad you're here. We're asked to identify if the given relation represents a function then determine its domain and range. Then we're given an XY table. It has two columns. The first column is the X column. The second column is the Y column. And then beneath that are three rows. The first row has values of zero for X and zero for Y. The second row has values of negative 19 for X and 19 for Y. And the third row has values of negative 41 for X and for Y. Looking at our answer choices. Answer choice A is yes. For a function, a domain of 0 and a range of zero negative 19 negative 41 answer. Choice B yes, it is a function, a domain of zero, negative 19, negative 41 and a range of 1941. Answer trace C not a function domain of 0 1941 and a range of negative 19 negative 41. And answer choice D not a function domain of zero, negative 19, negative 41 and a range of 1941. All right. So first question, does this represent a function or not? And the technical answer for, if something's a function we ask ourselves, is this true for each distinct input? There is exactly one output. So what does that mean? Well, the input, those are the X values and so for each distinct X value, there should be exactly one output. Those are the Y values. Now, in practical terms, when we have a table like this, we need to ask ourselves, do any of the X values repeat and no, they do not zero, negative 19, negative 41. None of those repeat. OK. That's a good start. And the other question is for each of those X values, do they have multiple Y values listed? And no, they do not. Each X value, they're all distinct has exactly one Y value associated with it. So they're distinct and there's only one output for each. So yes, this is a function. Yay. Happy day. We've got a function now determine its domain and range. Well, we recall from previous lessons that the domain is all of the possible X values and the range is all of the possible Y values. So for listing our domain, we put that squiggly line and then our first X value is zero, the next X value is negative 19 and the next X value is negative 41. Then we end that with the squiggly line for our range. Put the squiggly line. The first Y value listed is zero. The next one listed is 19 and the last one listed is 41. Then we put that squiggly line and those are our solutions. We look at our answer choices and this matches with answer choice. B well done. We'll catch you on the next one.

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Determine whether each relation defines a function, and give the domain and range. See Examples 1 – 4. x y 0 0 -1 1 -2 2