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.

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 a graph. We have a vertical Y axis, a horizontal X axis, they come together at the origin. And then on top of that graph, we have a straight line. The straight line is heading toward negative infinity for both X and Y. In the third quadrant, it passes through the X axis at negative 10 and then it continues for a little bit heading up through the second quadrant, passing through the Y axis at 03 and then heading up toward positive infinity for the X and Y values in the first quadrant. Our answer choices are answer choice. A not a function domain. Open parentheses, negative four to positive four closed parentheses range, open parentheses, negative four to positive four closed parentheses. Answer choice B not a function domain, open parentheses negative infinity to positive infinity, closed parentheses range, open parenthesis, negative infinity to positive infinity, closed parentheses. Answer choice C A function domain, open parentheses negative four to positive four closed parentheses and range open parentheses negative four to positive four closed parentheses and answer choice D function domain, open parentheses, negative infinity to positive infinity, closed parentheses and range open parentheses, negative infinity to positive infinity, close parentheses. All right. So when we're given a graph, we recall from previous lessons that we can test whether something is a function or not using the vertical line test, meaning that we are going to draw vertical straight up and down lines and see if any of those lines intersects with our graph line more than once. So if we had a graph line that's curving through and it just goes through at one point, that's fine. But if it goes through twice with any vertical line, it is not a function. If we draw vertical straight up and down lines and everywhere, we could possibly draw those vertical lines, it only passes through the function line once. Well, the proposed function line once then yes, it is a function. So what have we got here? Let's try and try and draw some lines. We can draw a vertical line through X equals negative two that only intersects at once. We could draw a vertical line through X equals negative one only intersects at once. The Y axis is a vertical line only intersects it once anywhere we could possibly draw a line. It doesn't even have to be on a line. We're only intersecting with our proposed function line once. So yes, it is truly a function All right. So we figured out that this is a function. Now, what does it still mean and range? Well, we notice that at the end of our function line, there are arrows that's telling us that this continues forever. Now, the domain is all of the possible X values for our function line. And because this thing continues forever, it's heading all the way toward negative infinity and all the way to positive infinity, it can never actually get to infinity because infinity is not attainable. So we use open parentheses, we put open parentheses, negative infinity, comma infinity and close with the parentheses. That's our domain. That's all the possible X values and the range, all the possible Y values. Yeah, same thing. It's heading toward negative infinity and positive infinity. So again, open parentheses, negative infinity comma infinity, close parentheses. And that's our domain and range. We look at our answer choices and this matches with answer choice. D well done. We'll catch you on the next one.

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

Key Concepts

Function Definition

Domain and Range

Vertical Line Test

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