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chaotic_butterflies

  • one year ago

Compare the functions shown below: (picture below) Which function has the greatest y-intercept?

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  1. chaotic_butterflies
    • one year ago
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    @iambatman

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  2. ybarrap
    • one year ago
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    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
    • one year ago
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    I understand, but how do you get the function from the middle graph?

  4. chaotic_butterflies
    • one year ago
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    @ybarrap

  5. ybarrap
    • one year ago
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    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
    • one year ago
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    I got -5 and 7.13 for the other two... and I'm not sure which is smaller...

  7. chaotic_butterflies
    • one year ago
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    I mean I know what's smaller between -5 and 7.13 - but not cosine or sine

  8. ybarrap
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    Well it's one number off this time

  11. ybarrap
    • one year ago
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    note that $$ \cos -\pi = \cos \pi=-1 $$

  12. chaotic_butterflies
    • one year ago
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    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
    • one year ago
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    $$ 0-\pi = -\pi $$ right?

  14. chaotic_butterflies
    • one year ago
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    I didn't think that would be correct...

  15. chaotic_butterflies
    • one year ago
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    Well I just tested it on my calculator and that's true, I never knew that occurred.

  16. ybarrap
    • one year ago
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    |dw:1433628863181:dw|

  17. ybarrap
    • one year ago
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    |dw:1433629021890:dw|

  18. chaotic_butterflies
    • one year ago
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    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
    • one year ago
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    Oh I see whatcha did there!

  20. ybarrap
    • one year ago
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    |dw:1433629149771:dw|

  21. ybarrap
    • one year ago
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    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
    • one year ago
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    |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
    • one year ago
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    I appreciate this so much.

  24. ybarrap
    • one year ago
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    no problem - so do you need more help with this one?

  25. chaotic_butterflies
    • one year ago
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    yes please, let me try to redo the middle one and I'd like for you to check it

  26. ybarrap
    • one year ago
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    Great!

  27. chaotic_butterflies
    • one year ago
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    Would it be -3?

  28. ybarrap
    • one year ago
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    The y-intercept of the middle graph is -3. Yes!

  29. chaotic_butterflies
    • one year ago
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    Yay!

  30. chaotic_butterflies
    • one year ago
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    Thank you Chris Evans guy!

  31. ybarrap
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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  35. ybarrap
    • one year ago
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    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
    • one year ago
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    Did we not just do all of that??

  37. ybarrap
    • one year ago
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    What did you get for f(0),g(0) and h(0)?

  38. chaotic_butterflies
    • one year ago
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    Doesn't f(0) mean that you set the x to 0 in the function? That's exactly what we did!

  39. ybarrap
    • one year ago
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    Yes, so f(0) was what?

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

  42. chaotic_butterflies
    • one year ago
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    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
    • one year ago
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    oh right the cos and pi thing

  44. chaotic_butterflies
    • one year ago
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    ?

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

  46. chaotic_butterflies
    • one year ago
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    So that leaves me with -2, and that's the greatest value!

  47. ybarrap
    • one year ago
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    -2+4=2

  48. chaotic_butterflies
    • one year ago
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    Herp a derp, I knew that >.<

  49. chaotic_butterflies
    • one year ago
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    Thank you so much!

  50. ybarrap
    • one year ago
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    yep, so f(0)=-5 g(0)=-3 h(0)=2 The order from smallest to largest: -5<-3<2

  51. chaotic_butterflies
    • one year ago
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    yay!

  52. ybarrap
    • one year ago
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    good job :)

  53. chaotic_butterflies
    • one year ago
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    Why thank you Mr. Evans.

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