Sign In
When applying a transformation to a function just after another took place, there are some cases where the order in which we apply transformations is important and in others it is not. We will consider the parent function f(x)=x5 to discuss both cases, one at a time.
Suppose that we want to apply a horizontal translation and a reflection in the x-axis to f(x)=x5. In this case the order in which we apply them is not important, since the resulting offspring function will be the same in both cases. We can see this in the graphs shown below.
Another example is applying a vertical stretch and a reflection in the x-axis.
Notice that these are just some examples, as there are other combinations of transformations where the order does not matter.
If we now consider applying a horizontal translation and a reflection in the y-axis to to f(x)=x5, then the order in which we apply them is important. Note that the resulting offspring function will not be necessarily the same in both cases. We can see this in the graphs shown below.
Similarly, when doing a vertical translation and a reflection in the x-axis, the order matters.