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Homework Help: Graphing (precalculus)

  1. Jun 30, 2010 #1
    1. The problem statement, all variables and given/known data
    Sketch the graph of the function y=(x-3)^2 by transforming the graph of an appropriate function of the form y=x^n



    2. Relevant equations
    y=(x-3)^2, y=x^n


    3. The attempt at a solution
    Precisely speaking, im just totally confused with what the question is asking. i mean i know how to graph y=(x-3)^2 bit idk what the y=x^n is about. thanks so much!
     
  2. jcsd
  3. Jun 30, 2010 #2

    CompuChip

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    If you look carefully at the exponents, you might guess that they mean n = 2.
    So the question is, through what (geometric) operation(s) can you obtain the graph of (x - 3)3 from that of x2?

    Since x2 is a basic graph (you should be able to draw it by heart), given this set of operations you can also draw (x - 3)2.
     
  4. Jun 30, 2010 #3

    HallsofIvy

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    Generally speaking, anything that is done to x before the "basic function" is a change in x and so changes the graph horizontally. Anything that is done after the "basic function" is a change in y and so changes the graph vertically.

    Here, the "basic function" is [itex]x^2[/itex] and [itex](x- 3)^2[/itex] is just [itex]x^2[/itex] with 3 subtracted from x before the square. The graph of [itex]y= x^2[/itex] itself is a parabola with vertex at (0, 0). x- 3= 0 when x= 3. The graph of [itex]y= (x- 3)^2[/itex] is the graph of [itex]y= x^2[/tex] shifted three places to the right- a parabola with vertex at (3, 0).
     
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