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Math Help - Transformations of graphs!

  1. #1
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    Transformations of graphs!

    The graph of y=sqrt(3x-x^2) is given. Use transformations to create a function whose graph is as shown.



    1.)
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  2. #2
    No one in Particular VonNemo19's Avatar
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    It looks like a reflection in the x axis (ie f(x)=-y) followed by vertical (1unit down) and horizontal (4 units back) shifts in the negative direction.
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  3. #3
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    Quote Originally Posted by VonNemo19 View Post
    It looks like a reflection in the x axis followed by vertical (1unit down) and horizontal 4 units back) shifts in the negative direction.
    I'm trying to find the equation but I keep getting the wrong answer.

    Here's the answer if it helps. I just don't know how to get that answer.
    1) y= -sqrt(-x^2-5x-4)-1

    Help!
    Last edited by yoman360; July 11th 2009 at 03:34 PM. Reason: To add more detail
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  4. #4
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by yoman360 View Post
    I'm trying to find the equation but I keep getting the wrong answer.

    Here's the answer if it helps. I just don't know how to get that answer.
    1) y= -sqrt(-x^2-5x-4)-1

    Help!
    If I had y=\sqrt{x}. To flip it through the x axis I'd tack on a negative like so

    y=-\sqrt{x}

    If I wanted to slide it to the left 4 units I'd add four to the variable like this

    y=-\sqrt{(x+4)}

    If I then wanted it to shift down a unit I'd add a constant (subtract in this case)

    y=-\sqrt{(x+4)}-1

    Get it?
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  5. #5
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    Quote Originally Posted by VonNemo19 View Post
    If I had y=\sqrt{x}. To flip it through the x axis I'd tack on a negative like so

    y=-\sqrt{x}

    If I wanted to slide it to the left 4 units I'd add four to the variable like this

    y=-\sqrt{(x+4)}

    If I then wanted it to shift down a unit I'd add a constant (subtract in this case)

    y=-\sqrt{(x+4)}-1

    Get it?
    Ok I get it now I'm gonna try and see if I can get the answer. I'll put a post to tell you if i get it right or not.
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  6. #6
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by yoman360 View Post
    Ok I get it now I'm gonna try and see if I can get the answer. I'll put a post to tell you if i get it right or not.
    Sounds like a plan.
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  7. #7
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    Ah I didn't get it right
    this is what i did!
    y= sqrt(3x-x^2)
    y= sqrt(-(3x-x^2))
    y= -(sqrt(-(3x-x^2)))
    y= -(sqrt(-(3x-x^2+1)))-1
    My answer: y= - sqrt(-3x+x^2+1) - 1

    correct answer: y=-sqrt(-x^2-5x-4)-1

    what did I do incorrectly?
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  8. #8
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by yoman360 View Post
    what did I do incorrectly?
    Since you gave it the old college try I'll do it for you.

    y=-\sqrt{3(x+4)-(x+4)^2}-1
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  9. #9
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    Quote Originally Posted by VonNemo19 View Post
    Since you gave it the old college try I'll do it for you.

    y=-\sqrt{3(x+4)-(x+4)^2}-1
    Thanks! But I don't understand how you got that.
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  10. #10
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by yoman360 View Post
    Thanks! But I don't understand how you got that.
    To flip it, I tacked on the negative.

    To slide to the left, i added 4 wherever i saw an x.

    to slide it down, i subtracted 1 from everything.
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  11. #11
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    Quote Originally Posted by VonNemo19 View Post
    To flip it, I tacked on the negative.

    To slide to the left, i added 4 wherever i saw an x.

    to slide it down, i subtracted 1 from everything.
    Oh thanks thats why! I relected y axis then shifted to the left 1 then reflected x axis then shift down 1.
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  12. #12
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    Quote Originally Posted by yoman360 View Post
    Thanks! But I don't understand how you got that.
    First 'move' it back 4 units by using (x+4) for x.

    Flip it by multipling by -1.

    'Move' it down by subtracting 1.
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  13. #13
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by yoman360 View Post
    Oh thanks.
    You're welcome. You can click them buttons whenever you feel like it yoman.
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