ValentinaT Group Title Can someone show me how to graph xy = 15? one year ago one year ago

1. e.mccormick Group Title

Find y, graph a few points, like the y intercept. and watch out for x=0.

2. e.mccormick Group Title

Oh, and finding the y intercept is actually a bit of a trick.... you may notice there is not one. There is also not an x intercept.

3. e.mccormick Group Title

When you solve for y, you get: $$y=\frac{15}{x}$$ Any x that evenly divides 15 is a good point to use. So $$x=\{-3,-1.5,1.5,3\}$$ give useful points.

4. ValentinaT Group Title

Okay.

5. e.mccormick Group Title

Then play connect the dots. Remember, you can't cross either the x or y axis.

6. e.mccormick Group Title

(1,15), (15,1), (-1,-15), (-15,-1) are also there, so you have an idea what happens to the tails.

7. e.mccormick Group Title

The lack of an x or y intercept is one of the big clues to the shape. Do you know what that means? What quadrants your points are in is the other part of this clue.

8. ValentinaT Group Title

9. e.mccormick Group Title
10. ValentinaT Group Title

Thanks!

11. ValentinaT Group Title

Could you help me with one more?

12. e.mccormick Group Title

Sure, but first... one concept from this type graph becomes super important later in math. Can you guess why the graph shoots up and down as it gets close to the origin?

13. ValentinaT Group Title

Not exactly sure.

14. ValentinaT Group Title

Because it is undefined?

15. e.mccormick Group Title

$$y=\frac{15}{x}$$ Well, what if x is really small? Close to 0. Say $$x=\frac{1}{100}$$ $y=\frac{15}{\frac{1}{100}}\\ y=\frac{15}{1}\cdot\frac{100}{1}\\ y=1500$

16. ValentinaT Group Title

Oh, okay.

17. e.mccormick Group Title

The undefined part then becomes what they call an asymptote. Vertical asymptotes are lines that can not be crossed.

18. ValentinaT Group Title

Alright. One more problem?

19. e.mccormick Group Title

Sure.

20. ValentinaT Group Title

Okay. $y = \frac{ -18 }{ x }$

21. e.mccormick Group Title

Same principal.

22. e.mccormick Group Title

It just changes what quads because of the -.

23. ValentinaT Group Title

24. e.mccormick Group Title

The important thing for easy graphing of these are factors of 18. Half points are not bad, but sometimes when you get down to weird numbers it just gets hard to graph nicely. 18 9 6 3 2 1 are all factors of 18. So they make the "easy" points this time. 1.8 is OK, just not as easy to graph as whole numbers and halfs.

25. ValentinaT Group Title

Okay.

26. e.mccormick Group Title

And you will get something like:|dw:1368216529907:dw|Not to scale this time, but I am sure that you get the point by now.

27. ValentinaT Group Title

For some reason -1.8,-10 and 1.8,10 aren't plotting right, I know you said it would be a bit harder.

28. e.mccormick Group Title

(-1.8,10),(1.8,-10)

29. ValentinaT Group Title

Yeah, I just realized I did it wrong, thanks.

30. e.mccormick Group Title

np. Have fun!

31. ValentinaT Group Title

32. ValentinaT Group Title

Thanks for the help!

33. e.mccormick Group Title

Yah, not too terrible once you have the basic concept.