The key transformations include translations, reflections, stretches, and compressions. Understand how these affect the graph of a function, both horizontally and vertically.
A vertical translation by *c* units is represented by *f(x) + c*. A horizontal translation by *c* units is represented by *f(x - c)*.
Reflection in the x-axis changes *f(x)* to *-f(x)*, while reflection in the y-axis changes *f(x)* to *f(-x)*.
Vertical stretch/compression by a factor of *k* is represented by *kf(x)*. Horizontal stretch/compression by a factor of *k* is represented by *f(x/k)*.
Follow the order of operations (PEMDAS/BODMAS) in reverse. Address horizontal shifts first, then stretches/compressions, reflections, and finally vertical shifts.
Invariant points are points that remain unchanged after a transformation. Identifying them can help you accurately sketch the transformed graph. For example, points on the x-axis are invariant under reflection about the x-axis.
Input both the original function and the transformed function into your calculator and compare their graphs. This can help you visually confirm that the transformations have been applied correctly.
Common mistakes include incorrect application of horizontal transformations (remembering the negative sign), mixing up vertical and horizontal transformations, and not applying the correct order of transformations.
Your textbook, lecture notes, and tutorial worksheets are excellent resources. Consider seeking H2 Math tuition for personalized guidance and additional practice. Online resources and past year papers can also be beneficial.