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anonymous

  • one year ago

In what direction and by how many units is the graph of f(x) = 6 sin(2x + π) − 5 vertically and horizontally shifted?

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  1. anonymous
    • one year ago
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    I believe the vertical shift is down 5, but I don't know about the horizontal shift.

  2. amistre64
    • one year ago
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    when does the argument for sin equal zero?

  3. amistre64
    • one year ago
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    in other words y = sin(x) is the parent function its 'center' is defined when x=0 to know how for it shifts on the x axis, the argument of x gets adjusted to read: 2x+pi so when does 2x+pi = 0?

  4. anonymous
    • one year ago
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    wait, sorry. this lesson confused me a lot. am i supposed to get x alone in 2x+pi=0?

  5. amistre64
    • one year ago
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    yes

  6. anonymous
    • one year ago
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    so it would be x= -pi/2 ?

  7. amistre64
    • one year ago
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    correct so our normal value at x=0, has now been shifted over to x=-pi/2

  8. anonymous
    • one year ago
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    so the answer would be down 5 and left pi/2?

  9. amistre64
    • one year ago
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    yep

  10. anonymous
    • one year ago
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    alright thank you! do you think you could help me with one more problem?

  11. amistre64
    • one year ago
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    one more, sure, if my sanity holds

  12. anonymous
    • one year ago
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    Which of the following functions has the greatest y-intercept?

  13. amistre64
    • one year ago
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    tell me your thoughts on how to approach it

  14. anonymous
    • one year ago
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    i honestly have no idea i'm sorry. please don't lose your sanity lol

  15. amistre64
    • one year ago
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    what would you say is the value of x for all points on the y axis?

  16. anonymous
    • one year ago
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    doesn't the x value vary depending on what the y is?

  17. amistre64
    • one year ago
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    |dw:1433275550605:dw| where do we generally put the y axis? for what value of x does it pass thru?

  18. amistre64
    • one year ago
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    do not confuse a function, for how we measure the function. the function is a curve, for a given value of x, we can measure how far the curve is from the x axis, by comparing it against the y axis. say we have a function that measures the height of a tree at a given day. the tree is the object that we are measuring (it is the function) the height of the tree is NOT the function, it is how we are measuring it. (the y axis)

  19. amistre64
    • one year ago
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    if we want to know WHERE the function intersects (crosses over or hits) the y axis ... we should be cognizant of where the y axis is to start with. right?

  20. anonymous
    • one year ago
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    the y axis usually passes through the 0 on the x axis

  21. amistre64
    • one year ago
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    got caught in a spin cycle ... but yes, it passes thru where x=0

  22. amistre64
    • one year ago
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    so, lets compare our functions, when x=0

  23. amistre64
    • one year ago
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    |dw:1433276240758:dw|

  24. anonymous
    • one year ago
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    so for the table, x=0 when y=0?

  25. amistre64
    • one year ago
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    more appropriately: y=0, when x=0, but yeah

  26. anonymous
    • one year ago
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    so the y-intercept of the f(x) table is 0?

  27. amistre64
    • one year ago
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    correct: f(0) = 0 g(0) is what?

  28. anonymous
    • one year ago
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    would it be -3? i think the number at the end is the y-intercept but i'm not sure

  29. amistre64
    • one year ago
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    its not the number on the end, is the value when x=0 which in this particular case g = 4 sin(4x) - 3 g = 4 sin(0) - 3 g = 0 - 3 is -3, but dont go by "last term", its not a good conjecture.

  30. amistre64
    • one year ago
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    what is the y intercept of: y = 2cos(x) + 1 ??

  31. anonymous
    • one year ago
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    3?

  32. amistre64
    • one year ago
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    yep, so "the last term" is not a valid approach is it?

  33. anonymous
    • one year ago
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    no, i see now though. so the y-intercept of f(x) would be the answer to that one?

  34. amistre64
    • one year ago
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    0 is more than -2, yes g(0) < f(0) -2 < 0

  35. amistre64
    • one year ago
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    or -3 depending on what keys we want to hit ...

  36. anonymous
    • one year ago
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    haha i understood it! thanks a lot for your help. i'm not too great with math but you were really patient so thank you!

  37. amistre64
    • one year ago
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    good luck :)

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