For homework before next class, answer the following question.
Does the order in which we apply transformations matter? For example, if I begin with the graph of \(y=f(x)\), and I
- (A) translate by 2 units to the left, and then
- (B) stretch vertically by a factor of 3,
will I always get the same result as I would if I had begun with the graph of \(y=f(x)\), and I
- (B) stretch vertically by a factor of 3, and then
- (A) translate by 2 units to the left?
What if, instead of stretching vertically by a factor of 3, I stretch horizontally by a factor of 3? Does order matter in that case?
Consideration of the function \(f(x)=x^3-2x^2\) may help here.