Make sure a function is written in the form or before trying to interpret the function. When a function is written in a different form, such as or , the parameters will behave differently because a different order of operations is implied. The following table shows some examples of different possibilities. Can you think of other examples?

Function	Order of Operations Applied to y = f(x)	Used in This Course
	a and b then h and k	used in this course
	a and b then h and k	used in this course
	a then h then b then k	not explicitly used in this course
	b then k then a then h	not explicitly used in this course
	h and k then a and b	not explicitly used in this course

Order of Transformations illustrates the difference between and The second function is obtained if you translate before stretching and reflecting.

As you can see, and act very differently. This course focuses on the forms and

As in previous lessons, the process of sketching a function of the form from y = f(x) can be reversed to determine an equation given the graph of f(x) and an image of the graph. The next two examples describe this process.

Watch Determining an Equation from a Graph.

Read “Example 3” on page 37 of the textbook. This example illustrates how to determine the equation of a function by looking at how individual points are mapped.

Self-Check 3

1. Complete “Your Turn” from “Example 3” on page 38 of the textbook. Answer
2. Complete “Check Your Understanding” questions 4.a., 10.a., and 13 on pages 39 and 40 of the textbook. Answer

Add the following formula to your copy of Formula Sheet: