## chaotic_butterflies one year ago Compare the functions shown below: (picture below) Which function has the greatest y-intercept?

1. chaotic_butterflies

@iambatman

2. ybarrap

Set x= to zero and compare value of the two functions. When you set x=0, the function is crossing the y-axis - hence the term, "y-intercept." Recall that cos(0) = 1 and cos(0 - pi) = cos (-pi) = -1

3. chaotic_butterflies

I understand, but how do you get the function from the middle graph?

4. chaotic_butterflies

@ybarrap

5. ybarrap

If you want to find the function that matches the middle graph you need to first determine for this function, whether you are going to use cosine or sine. Which function, cosine or sine, is smaller at x=0?

6. chaotic_butterflies

I got -5 and 7.13 for the other two... and I'm not sure which is smaller...

7. chaotic_butterflies

I mean I know what's smaller between -5 and 7.13 - but not cosine or sine

8. ybarrap

Which of these is similar to the function in your middle graph: |dw:1433628050735:dw| To determine which is small between -5 and 7.13 use the number line |dw:1433628325169:dw| I don't know how you got 7.13 from the second function.

9. chaotic_butterflies

I'm thinking sine... and I'll explain. h(x) = 2 cos(2x − π) + 4 h(x) = 2 cos(0 − π) + 4 h(x) = 2 cos(π) + 4 h(x) = 2 cos(π) + 4 h(x) = 0.99..(3.14) + 4 h(x) = 4.13 + 4 h(x) = 8.13

10. chaotic_butterflies

Well it's one number off this time

11. ybarrap

note that $$\cos -\pi = \cos \pi=-1$$

12. chaotic_butterflies

but would it be negative pi because it's just being subtracted from 0 which is nothing - so if you take nothing away from something, that doesn't alter it...

13. ybarrap

$$0-\pi = -\pi$$ right?

14. chaotic_butterflies

I didn't think that would be correct...

15. chaotic_butterflies

Well I just tested it on my calculator and that's true, I never knew that occurred.

16. ybarrap

|dw:1433628863181:dw|

17. ybarrap

|dw:1433629021890:dw|

18. chaotic_butterflies

OH MY GOSH I FEEL SO STUPID I COULD GET THE Y INTERCEPT FROM THE MIDDLE BY JUST LOOKING AT THE GRAPH /)-_-

19. chaotic_butterflies

Oh I see whatcha did there!

20. ybarrap

|dw:1433629149771:dw|

21. ybarrap

Yes, if you want the y-intercept, look at the graph where x=0, that's where the graph "intercepts" the y-axis

22. ybarrap

|dw:1433629403543:dw| See how one is rotating counter clockwise and the other is rotating clockwise by 180 degrees but in the end, both are facing YOU!

23. chaotic_butterflies

I appreciate this so much.

24. ybarrap

no problem - so do you need more help with this one?

25. chaotic_butterflies

yes please, let me try to redo the middle one and I'd like for you to check it

26. ybarrap

Great!

27. chaotic_butterflies

Would it be -3?

28. ybarrap

The y-intercept of the middle graph is -3. Yes!

29. chaotic_butterflies

Yay!

30. chaotic_butterflies

Thank you Chris Evans guy!

31. ybarrap

There seems to be a few things you've asked here: y-intercept, graph of the function, which function has biggest y-intercept. Not sure which you are solving. brb

32. chaotic_butterflies

I was just trying to figure out what the greatest y intercept was, but I had questions within the question which you answered

33. chaotic_butterflies

But wait, my options don't allow me to pick both g(x) and h(x), yet they both have the same y intercept which is larger than -5..

34. chaotic_butterflies

35. ybarrap

Ok, now I see the whole problem now, LOL It's asking which functions, f(x), g(x) , h(x) or all have the greatest y-intercept (i.e. which has the largest value of y when x=0): $$f(0)\\ g(0)\\ h(0)$$ What is f(0)? What is g(0)? What is h(0)?

36. chaotic_butterflies

Did we not just do all of that??

37. ybarrap

What did you get for f(0),g(0) and h(0)?

38. chaotic_butterflies

Doesn't f(0) mean that you set the x to 0 in the function? That's exactly what we did!

39. ybarrap

Yes, so f(0) was what?

40. ybarrap

I see that you've highlighted f(0)=-5,g(0)=-3 and maybe h(0)=-3. The last one is not correct. Once you get all these right, compare them and take the max.

41. chaotic_butterflies

Oh, the last one was the one you corrected me on and I redid, I'll do it again then.

42. chaotic_butterflies

h(x) = 2 cos(2x − π) + 4 h(x) = 2 cos(− π) + 4 h(x) = - 3.13 + 4 h(x) = 0.86 Oh wow that's wayy different...

43. chaotic_butterflies

oh right the cos and pi thing

44. chaotic_butterflies

?

45. ybarrap

$$h(0) = 2 \cos(2\times0 − \pi) + 4\\ h(0) = 2 \cos(−\pi) + 4\\ h(0) = 2\times \color{red}{-1} + 4\\ h(0) = -2+4\\$$ http://www.wolframalpha.com/input/?i=cos%28-pi%29

46. chaotic_butterflies

So that leaves me with -2, and that's the greatest value!

47. ybarrap

-2+4=2

48. chaotic_butterflies

Herp a derp, I knew that >.<

49. chaotic_butterflies

Thank you so much!

50. ybarrap

yep, so f(0)=-5 g(0)=-3 h(0)=2 The order from smallest to largest: -5<-3<2

51. chaotic_butterflies

yay!

52. ybarrap

good job :)

53. chaotic_butterflies

Why thank you Mr. Evans.