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Trigonometric graph transformation

  1. Mar 9, 2017 #1
    1. The problem statement, all variables and given/known data
    Transform the following equation:

    X2sin(3x)

    1. Stretch vertically by a factor 9
    2. Stretch horizontally by a factor 3
    3. Shift to the left by a value of 1.


    2. The attempt at a solution
    1. Stretching vertically by a factor 9 gives:

    9x2sin(3x)

    2. Stretching vertically by factor 3 is done by dividing 3x by 3, so I get

    9x2sin(x)


    3. Shifting one to the left gives (I think I am going wrong here):

    9(x+1)2sin(x+1)

    Which can be simplified into:

    (9x2+18x+9)sin(x+1)


    But this answer is wrong. Where did I go wrong?
     
  2. jcsd
  3. Mar 9, 2017 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You do not have an equation; an equation has an "=" sign in it, and your expression does not. What you have is a function of x.

    I think the problem should be restated as follows. For the graph ##y = x^2 \sin 3x##:
    1. Stretch the graph vertically by a factor of 9.
    2. Stretch the graph horizontally by a factor of 3.
    3. Shift the graph to the left by 1 unit.

    Your solution of 1 is correct: the stretched graph is ##y = 9 x^2 \sin 3x.##

    For 2: think about it: a point such as ##(k,y(k))## moves to ##(3k,y(k))## in the stretched graph, so if the old graph is ##y = f(x)## and the new graph is ##y = F(x)##, you can see how ##F(x)## must be related to the function ##f(x)##. You have it partly right, but not completely right.

    For 3: a point ##(k,f(k)## in the old graph moves to ##(k-1, f(k)## in the new graph. From that, you can get the equation ##y = F(x)## of the new graph in terms of the old graph ##y = f(x).##
     
  4. Mar 9, 2017 #3

    Mark44

    Staff: Mentor

    I agree complete with what Ray already said: you do not have an equation here.
    You should have an equation here. Specifically, ##y = 9x^2 \sin(3x)##.
    Again, this should be an equation. Also, you wrote "stretching vertically by a factor 3" -- the stretch is supposed to be horizontally by a factor of 3. You need to be working with ##y=x^2\sin(3x)##
    Should be an equation. Start with ##y = x^2\sin(3x)##, and shift it to the left by 1 unit.
    Aside from being incorrect, you didn't really simplify it by expanding ##(x + 1)^2##.
     
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