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Homework Help: Transforming Graphs?

  1. Jan 21, 2008 #1
    Some questions about transforming graphs that I would like a hand with. I've given them educational guesses, but if someone could take a look at them, that would be great.

    1. The problem statement, all variables and given/known data

    2. Explain the difference in the transformations to the graph of f(x) by f(x+2) and f(x)+2.

    3. Explain the difference in the transformations to the graph of f(x) by f(3x) and 3f(x).

    5. Explain how to find an equation of the normal to a curve at a given point.

    2. Relevant equations

    None

    3. The attempt at a solution

    For (2) f(x+2) would stretch the graph along the X axis by x2, right? Where as f(x)+2 would just nudge the graph along the X axis by 2 points.

    But for (3) I'm really not sure what the difference is (obviously there is a significant one) of the 3 being inside the brackets or out. Any help here?

    For (5)... I'm a little stuck. I'm thinking that I might have to differentiate to start with, but I'm not entirely sure.

    Thanks for taking the time to look at this.
     
  2. jcsd
  3. Jan 21, 2008 #2
    5.
    1.differentiate
    2. find the slope/gradient (tangent line)
    3. find the normal gradient (tangent slope x normal slope = -1)
    4. the coordinate of one point and the normal gradient are known, proceed with finding the line equation.
     
  4. Jan 21, 2008 #3
    2.

    f(x+2) : move the original graph two units to the left

    f(x) + 2 : move the original graph two units upwards
     
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