In Exercises 15–26, use graphs to find each set.

[3, ∞) ∩ (6, ∞)

Question

In Exercises 15–26, use graphs to find each set.

[3, ∞) ∩ (6, ∞)

Accepted Answer

Hello everyone in this video. We're going to be looking at this practice problem where we want to find the intersection between the intervals five in infinity and nine in infinity. And in order to make this easier. I'm going to draw graphs to represent my intervals and this will make it easier to see where they overlap. And I'm just going to go ahead and draw three graphs because I want my first graph to represent my first interval, my second graph to represent my second interval and my third graph to represent the intersection or where the two intervals intersect. And I'm going to go ahead and number my graphs from four 25, 6, 7, 8, 9, 10, 11, 12. And I want to try to make sure that my graphs look as similar as possible to one another to make it easier to compare them. So I'm going to make sure that all three of my graphs go from 4 to and once I do that I can start drawing my first interval And in this case my first interval is five to infinity. Notice that the five is a bracket and that goes all the way to infinity. So I'll leave it as an arrow and that will indicate to me that it goes to positive infinity. And my second interval is parentheses nine to infinity. So I'll draw parentheses at nine and that one also goes to infinity. So I need to find the range of values where the two intervals intersect and that means that both lines need to be existing. So the only space where I see that happening is past this point here. Because you can see that the blue line starts at nine. So that seems to be my lower bound. So when I write that in as parentheses, nine notice that I can see that easily because there's no blue line in this portion here. So my intersection clearly begins at nine and then it seems that both of them go to infinity, so the intersection doesn't ever stop. So I can write my intersection going to infinity as well. So now this is my intersection as a graph. And if I translate this to interval notation, I have nine to infinity. And this becomes my final intersection value. And you can see that this aligns with answer choice C. So hopefully this video helped and see you next time.

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