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← Domain - College Algebra

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Showing Revision 2 created 05/24/2016 by Udacity Robot.

  1. Remember that the reason Athena is creating all of these box models in the first
  2. place, is for her architecture internship. So, that means that when she's
  3. discussing functions like this one, she's probably going to want to focus on the
  4. values of the domain that make sense in the physical situation she's discussing.
  5. We figured out before, that if Athena wants to make sure, that she's actually
  6. able to fold her piece of paper into a box, x should be greater than zero. But
  7. it should also be less than 2.5 inches. However, we saw that if x equals zero,
  8. then the volume equals zero. And if x equals 2.5, the volume also equals 2.5.
  9. The idea of zero volume is actually pretty understandable. It's negative volume
  10. that's the issue. So, I'm going to go ahead and decide to include these
  11. endpoints in our domain. So, here we go. This is the domain of the function that
  12. we've decided upon, using our common sense to deal with the situation at hand.
  13. So, like we talked about in the last lesson, this is not a
  14. mathematically-imposed domain restriction. This is one that we're imposing upon
  15. the equation ourselves to make the equation better fit the situation of the box.
  16. So, let's visualize this with a graph using this domain restriction. So, here's
  17. what a graph of this function looks like with these domain restriction put in
  18. place. We can see that the graph is only allowed to take on values of x between
  19. 0 and 2.5. And as shown in this inequality, our interval includes these end
  20. points, so they are closed circles to either one.