In Exercises 15–26, use graphs to find each set.(- 3, 0) ∩ [- 1, ...

Question

In Exercises 15–26, use graphs to find each set.(- 3, 0) ∩ [- 1, 2]

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 two intervals negative 5-1 and negative 3-4. So in order to try and visualize this I'm going to use a number line graph to draw my intervals and in this case I want my number line to at least encompass the highest value in my interval. In this case -4 and my lowest value -5. So I'm gonna go ahead and start numbering it from negative six going up. And if I do that I'm left with a number line graph that goes from -6-5. So you can see that both four and negative five right here. So I have the range that I want and I'm gonna go ahead and start graphing my first interval which is negative 5 to 1. So I have bracket negative five or parentheses negative 52, parentheses one. So that's my first interval. And then I'm gonna draw a second number line with the same number lines are the same ticks for numbers as my first number line to draw my second interval on. And I wanted to look as similar as possible to my first number line because I want to be able to compare the two intervals. So you can see that it's also a number line that goes from negative 6-5. But I'm gonna use it to draw my second interval negative 3-4. And in this case you can see that it's bracket negative three, 24 bracket. So if I connect those two, I have my second interval. And in this case I want to find the intersection of the two intervals. So I'm going to go ahead and draw a third number line to represent where those intervals intersect. And again I'm trying to draw it as similar as possible to my previous to in order to make it easier for me to compare. So once again it's the number line that goes from negative 6 to positive five. And I'm trying to find the intersection so I need to find where the two intervals overlap and you can see that my first interval sort of stops here or so. This is the upper bound, it seems for my first interval and it seems like that's where an intersection begins. So I'm going to go ahead and draw the parentheses at one to represent that upper bound And my lower bound seems to be at negative three Because my second interval starts at -3. So that becomes my lower bound And once I connect these that becomes a range of values where my two intervals intersect. And if I convert this to interval notation I have bracket negative three and one parentheses. So this becomes my intersection. And you can see that this alliance with answer choice B. So hopefully this video helped and see you next time

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In Exercises 15–26, use graphs to find each set.(- 3, 0) ∩ [- 1, 2]

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