Overview
On this page, you will find resources to review how to modify ("transform") and combine functions in various ways to construct new ones, including piecewisedefined functions and rational functions.
Remember that it is up to you to decide how much of the listed resources you need to read or watch, you probably do not need to go through all of it. You might also want to look at the General Study Tips & Tricks page for some recommendations on how to effectively study with a math textbook and videos.
To Read

Read everything up to subsection 0.3.4 (Inverse Functions) of: http://mathquest.carroll.edu/CarrollActiveCalculus/S_0_3_Transformations.html
and make sure to work on at least the following:
 Preview Activity 0.3.1
 Activity 0.3.2
 Activity 0.3.3
 Activity 0.3.4

Read all of: http://mathquest.carroll.edu/CarrollActiveCalculus/S_0_6_PowersPolysRationals.html
and make sure to work on at least the following:
 Activity 0.6.2
 Example 0.6.1
 Activity 0.6.3
 Activity 0.6.4
 Activity 0.6.5
To Watch

Watch this video which explains how we calculate composite functions to obtain other functions:

Watch these two videos which explain how to graph piecewisedefined functions:

Watch this short video about the symmetries of even or odd functions:

Watch this video about the end behaviour of polynomials: