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anonymous

  • one year ago

What of the following statements have the same result? f(1) when f(x) = 5x + 1 f−1(3) when f(x) = 2x+3 3y − 7 = y + 5

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  1. anonymous
    • one year ago
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    @jim_thompson5910

  2. jim_thompson5910
    • one year ago
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    f(x) = 5x + 1 f(1) = 5(1) + 1 ... replace every x with 1 f(1) = ???

  3. anonymous
    • one year ago
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    5

  4. jim_thompson5910
    • one year ago
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    close but no

  5. anonymous
    • one year ago
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    6 lol

  6. jim_thompson5910
    • one year ago
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    "5(1) + 1" means "5 times 1 plus 1"

  7. jim_thompson5910
    • one year ago
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    yeah f(1) = 6

  8. jim_thompson5910
    • one year ago
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    "f−1(3) when f(x) = 2x+3" is a fancy way of saying "plug in f(x) = 3 and solve for x" f(x) = 2x+3 3 = 2x+3 3-3 = 2x+3-3 ... Subtract 3 from both sides. 0 = 2x x = ???

  9. anonymous
    • one year ago
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    0

  10. jim_thompson5910
    • one year ago
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    yep x = 0 leads to f(x) = 3

  11. jim_thompson5910
    • one year ago
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    solve 3y − 7 = y + 5 for y. Tell me what you get

  12. anonymous
    • one year ago
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    6

  13. jim_thompson5910
    • one year ago
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    y = 6 is correct

  14. jim_thompson5910
    • one year ago
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    from part a) we got f(1) = 6

  15. anonymous
    • one year ago
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    ok so 1 and 3 :)

  16. jim_thompson5910
    • one year ago
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    yeah

  17. anonymous
    • one year ago
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    I have one last one and I'm done for tonight!

  18. jim_thompson5910
    • one year ago
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    show me what you have so far

  19. anonymous
    • one year ago
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    Ok. so I guess a positive end behavior for f(x)+2

  20. anonymous
    • one year ago
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    yes?

  21. jim_thompson5910
    • one year ago
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    how do you know it's positive?

  22. anonymous
    • one year ago
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    i just assumbed bc the leading co. is positive

  23. jim_thompson5910
    • one year ago
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    we don't know anything about the original function f(x). So we can't say if it has positive or negative end behavior

  24. jim_thompson5910
    • one year ago
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    what we can say is that the end behavior won't change if we add 2 to f(x)

  25. anonymous
    • one year ago
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    true. I agree

  26. jim_thompson5910
    • one year ago
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    f(x)+2 just shifts f(x) up 2 units

  27. jim_thompson5910
    • one year ago
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    on the other hand (-1/2)*f(x) flips f(x) over the x axis and compresses it vertically by a factor of 2

  28. jim_thompson5910
    • one year ago
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    so (-1/2)*f(x) will have its end behavior flipped

  29. anonymous
    • one year ago
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    I agree.

  30. jim_thompson5910
    • one year ago
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    what can you say about the y-intercept?

  31. anonymous
    • one year ago
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    It would be (0,2)

  32. jim_thompson5910
    • one year ago
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    but do we know what the y-intercept of f(x) is?

  33. anonymous
    • one year ago
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    and increasing?

  34. anonymous
    • one year ago
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    2

  35. jim_thompson5910
    • one year ago
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    we don't know what the y-intercept of f(x) is

  36. jim_thompson5910
    • one year ago
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    but whatever it is, it is shifted up 2 units for f(x)+2

  37. anonymous
    • one year ago
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    yes. And what about the -1/2 one?

  38. anonymous
    • one year ago
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    so a wide parabola?

  39. jim_thompson5910
    • one year ago
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    it gets wider when you compress it vertically, yes

  40. anonymous
    • one year ago
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    But I don't understand how it is increasing and the regions where it does part>>

  41. anonymous
    • one year ago
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    any ideas?

  42. jim_thompson5910
    • one year ago
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    f(x) isn't given, so we cannot find the increasing/decreasing intervals. Whatever they are, they don't change when going to f(x)+2. Everything shifts up which is why the intervals don't change

  43. jim_thompson5910
    • one year ago
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    with (-1/2)*f(x), the intervals swap. Whatever was decreasing is now increasing and vice versa.

  44. anonymous
    • one year ago
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    Oh:O !! That makes sooo much more sense! Thanks:)

  45. anonymous
    • one year ago
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    is that it? We are done with the question

  46. jim_thompson5910
    • one year ago
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    yeah I think so

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