# Trigonometric graph transformation

1. Mar 9, 2017

### ArjenB

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. Mar 9, 2017

### Ray Vickson

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 $y = f(x).$

3. Mar 9, 2017

### 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 $(x + 1)^2$.