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 union between the two intervals 5 to Infinity and 9 to Infinity. And in this case I'm going to draw a number line to try and visualize these intervals and I'm drawing my number line with enough lines that I can represent both of these intervals. Actually I'll go ahead and draw three number lines because I want one for my first interval, I want one for my second interval and then I want one to represent the union of the two intervals. So I'll start numbering my graphs at four and then increase them. So 45678, 9, 10, 11, 12, 13, 14 and 15. And I'll do that for all of my graphs because I want them to try to look as similar as possible so I can compare them easier. And once I'm done with that you can see I have three very similar looking number lines where I can start drawing my intervals. So my first interval is bracket five. So I'm gonna go ahead and draw the bracket and it goes all the way to infinity. So I'm just going to draw it as a line that goes past my number line and keep it as an arrow so that I know it goes to infinity. My second interval is a parentheses nine and that one also goes all the way to infinity. So I'm gonna go ahead and draw the arrow and I want to find a range of values that represents both of these intervals. So I could start it four and go all the way but notice that none of my ranges have any values in this position. So this range wouldn't really describe them well. So I need to find my range that has the lowest value. And in this case it seems to be my first range, starting with the five. So I'm going to go ahead and draw that bracket in. So now you can see I found the lower bound of my union. Now I need to find the upper bound. Well in this case they both have this arrow that's telling me that they're going to infinity. So that means that my union also needs to go to infinity since there's no upper bound for either of the intervals. So this becomes my union of the two intervals. And if I represent that in interval notation, I have bracket five to positive infinity parentheses. So this becomes my final answer for the union. And you can see that this aligns with answer choice D. So hopefully this video helped and see you next time

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