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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

    Nathanael

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    Homework Helper

    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.

    Look:

    [itex]\sqrt[3]{-x}=\sqrt[3]{(-1)(x)}=\sqrt[3]{-1}\sqrt[3]{x}=-1\sqrt[3]{x}=-\sqrt[3]{x}[/itex]



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

    Mark44

    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 --
    $$\sqrt{x^3}$$
    or this --
    $$(\sqrt{x})^3$$

    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

    Nathanael

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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

    Nathanael

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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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