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

(- ∞, 5) ∩ [1, ...

Question

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

(- ∞, 5) ∩ [1, 8)

Accepted Answer

Hello. Everyone in this video we're going to be looking at this practice problem where we want to find the intersection of the intervals negative infinity to seven and 1-10. So in order to try to find this intersection more easily I'm going to draw number lines to represent my interval. So this first number line I'm going to use to represent my first interval negative infinity to seven. So I'll start numbering it from zero and I'll go up. So 0123456789. A lot a little bit more length to go up to 11. And I'm going to draw this graph another time because I want my second interval to also be represented on a graph. And I want that graph to look very similar to where I draw my first graph to make it easier to find the intersection between the two. So if I draw my first interval I have negative infinity to seven with a bracket at seven and I'll represent negative infinity by drawing an arrow letting me know that that's going to negative infinity. So that's my first interval. And I'll draw my second interval parentheses 1-10 on my second number line. So I'll do bracket one and parentheses 10. And then I'll connect that. And now I'm going to do a third number line to represent The intersection of those two. So it's gonna have the same numbering 0-11. And I want to find where my two intervals overlap and that range of values. So you can see that there's overlapping beginning here. This seems to be the lower bound at the one because that's where my second interval begins. So I'm going to say that's my lower bound and my upper bound maybe you think it's here because that's the highest value. But notice that there's no black line here, so I need to make sure that I choose an upper bound that works for both of my intervals. And you can see that's here at the seven. So I can draw it as a bracket as it's noted in my first interval. So this becomes my intersection and that's my intersection in graph format. So if I write this in interval notation, I'm left with Bracket one parentheses. So this becomes my final answer. And you can see that this aligns with answer choice B. So hopefully this video helped and see you next time.

In Exercises 15–26, use graphs to find each set. (- ∞, 5) ∩ [1, 8)

Key Concepts

Intervals

Intersection of Sets

Graphing Intervals

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