In Exercises 1–10, determine whether each relation is a function....

Question

In Exercises 1–10, determine whether each relation is a function. Give the domain and range for each relation. {(3, −2), (5, −2), (7, 1), (4, 9)}

Accepted Answer

Welcome back. I'm so glad you're here. We have this list of four ordered pairs and we're to determine if this relation is a function. So first let's list our ordered pairs, ordered pairs are set of parentheses, with an X. Value followed by a Y value. Our first ordered pair is seven negative five. Our next ordered pair is nine negative five. Our next ordered pair is 11 9. And our final ordered pair is 138. And to determine whether we have a function, we ask ourselves if for every value of X. Is there only one corresponding value of why? So we can start off with this first X value here for X equals seven. Is there only one corresponding value of Y? And yes, seven only shows up in this column once and the corresponding Y value is negative five for every value of X. Now let's look at X equals nine. Is there only one corresponding Y value? Yeah, because X only shows up here are X equals nine. Only shows up here one time. The corresponding y value is again negative five but that's fine. The Y value can show up more than one time. It's just that the X value can only show up once. Now for x equals 11, That's the only value where x equals 11 and the corresponding y value is nine. And so because the other ones have only shown up once. 13 only shows up once for our x value and the corresponding y value is eight. So yes, this is a function for every value of X. There's only one corresponding value of why? So now to figure out the domain and range, the domain is going to be all the possible values of X. Because we can list those 7, 9, 11 and 13. The range is going to be all the possible values of why and we don't need to repeat ourselves. So the range is going to be negative 59 and eight. Or you could have eight and nine. We look at our answer traces and this matches with answer choice C. Well done, we'll catch you on the next one.

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