Graphing Functions Using Vertical and Horizontal Shifts
In the next few sections, you will begin to strengthen your ability to graph functions without the aid of a graphing tool and without having to do a lot of algebra. You will learn some basic transformations that can be done to the graphs of the toolkit functions to make more complex functions. For example, we can take the graph of the square root function 
, shift it to the left or right, and determine the resulting equation. Conversely we can begin with the equation of 
and determine what has been done to the graph of without doing a lot of algebra.
Graphing Functions Using Vertical and Horizontal Shifts
Often when given a problem, we try to model the scenario using mathematics in the form of words, tables, graphs, and equations. One method we can employ is to adapt the basic graphs of the toolkit functions to build new models for a given scenario. There are systematic ways to alter functions to construct appropriate models for the problems we are trying to solve.