The previous chapter was about operations with functions. This chapter deals
primarily with operations *on* functions--that is, with operations that
alter the functions themselves.

The first section explains how to translate a function: to move it up, down, left, or right, without altering its shape, size, or dimensions. To move a function up or down, we alter the output of the function. To move a function left or right, we alter the input of the function. This section will explain both vertical shifts and horizontal shifts in detail.

The second section explains how to stretch and shrink a function--to increase or decrease its size without changing its proportions. To stretch and shrink in the horizontal direction, we alter the input of a function, and to stretch and shrink in the vertical direction, we alter the output of a function.

Next, this chapter explains how to reflect a graph across a line and rotate a graph around a point. As with the previous two transformations, we do this by changing the input and output of the function.

The final section provides a summary of all the transformations learned in the first three sections. It also explains how to combine transformations.

This is the first chapter that explores how to alter functions. This topic is important because understanding what happens to functions when we change their inputs and outputs aids in our understanding of the functions themselves.