Order is important because different graphs can be obtained depending on the order of the transformations are performed.

For instance, if the point is on original graph and there is a translation units up and then a reflection in the -axis, the resulting point will be .

However, if is reflected in the -axis first and translated units up, the resulting point will be .

Explanation:

Consider the point is on graph on .

There is two translations.

First translation units up.

Add to -coordinate.

.

Then a reflection in the -axis.

Multiply -coordinate by .

.

First reflection in the -axis.

Multiply -coordinate by .

.

Then translation units up.

Add to -coordinate.

.

Order is important because different graphs can be obtained depending on the order the transformations are performed.

For instance, if the point is on original graph and there is a translation units up and then a reflection in the -axis, the resulting point will be .

However, if is reflected in the -axis first and translated units up, the resulting point will be .