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Homework Help: Flipping Functions

  1. Aug 14, 2014 #1
    The problem shows two graphs, the first of which is just f(x)=3√x (square root of x cubed -not sure how to make it look like that-) and it wants me to give a function for the graph on the right.
    The second graph is flipped, vertically shifted 1 up f(x)+ 1 and horizontally shifted 2 right f(x-2).
    My problem is/was I can't determine if it is a vertical or horizontal flip because square root of x cubed looks the same both ways. So I have an assumption, I would like to know if it's correct and a question.

    It would have to be a vertical flip because a negative can be on the outside of a square root but not inside and still be a function?

    Also if I come across this problem again, and the horizontal and vertical flip would both look the same what are some better ways of determining which it is?
    Last edited: Aug 14, 2014
  2. jcsd
  3. Aug 14, 2014 #2


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    The square root of x cubed looks like this [itex]\sqrt{x^3}[/itex] but I'm assuming what you meant to say is the cube root of x? [itex]\sqrt[3]{x}[/itex] Like that?

    Not true. Since it's a cube root, you can have a negative inside of it with no complications.
    For example, the cube root of negative 8 is negative two, and the cube root of positive 8 is positive 2.

    It looks the same, because it IS the same. There is no difference between a horizontal and vertical flip (in this case)

    To flip it horizontally, you replace x with negative x (because you want to 'flip' the x axis) and so you get [itex]f(x)=\sqrt[3]{-x}[/itex]

    To flip it vertically you replace y (or "f(x)") with negative y (because you want to 'flip' the y axis) so you get [itex]f(x)=-\sqrt[3]{x}[/itex]

    Let's compare those two functions.
    Not only do they look the same visually (which is what is confusing you) but they ARE the same.



    So you see, it truly does not matter which way you do it. Not visually, and not mathematically.
  4. Aug 14, 2014 #3


    Staff: Mentor

    This is very confusing. You wrote 3√x, which is 3 times the square root of x. You described this as the square root of x cubed, which could be either this --
    or this --

    How you wrote it makes me think that you meant the cube root of x, which is ##\sqrt[3]{x}##. Which one is your problem?
  5. Aug 14, 2014 #4


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    What makes me even more certain that they meant [itex]\sqrt[3]{x}[/itex] is that they said (or implied) that the function is odd.
  6. Aug 14, 2014 #5
    I did mean cube root of X
    ty and sorry for the confusion

    your comparison was very helpful ty

    Where do I learn how to make the rest of the symbols, besides the 'Quick symbols' given
  7. Aug 14, 2014 #6


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    If you look at the top on the very right there's a sigma symbol [itex]\Sigma[/itex] which has a lot more symbols (it can sometimes be annoying to find what you're looking for at first)

    A lot of them are simple though, and so if you use them enough you'll just type it out by hand

    (for example, "x^2" gives you [itex]x^2[/itex])
  8. Aug 14, 2014 #7
    awesome thx again
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