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, -3), (-2, −2), (−1, −1), (0, 0)}

Accepted Answer

Welcome back. I'm so glad you're here. We are given four ordered pairs. This relation and were asked to figure out whether this relation is a function. So first to find out if we've got a function here, we're going to list are ordered pairs, ordered pairs, our X values followed by Y values in parentheses. So our first ordered pair is zero for X and zero for Y. Our next ordered pair gives us -4 for X and -4 for Y. Our next ordered pair gives us five for X and five for Y. And our final ordered pair gives us negative six for X and negative six for Y. And to ask ourselves whether we have a function we ask if for every X value, is there only one? Why value? So we can pick any X value for X equals zero. Is there only one y value? Yeah, there's only 10 listed here and that corresponds with the y value of zero for x equals negative four. Is there only one Y value negative four is only listed once here. And the Y value that corresponds with it is negative four for x equals five. Is there only one Y value? And yep. Likewise five is only listed once here for the X column. So for this corresponding y value, it's Y equals five and the same thing for our final one for x equals negative six. That's the only negative six value for X and there is exactly one corresponding Y value which is negative six. So yes, this is a function. Now we're asked to find its domain and range well the domain is going to be all of the possible X values, so we can put those in order negative six is the lowest, followed by negative four, then zero and five. The range is going to be all of the possible Y values, and likewise, starting with the lowest value, that's going to be negative six, negative 40 and five. 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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