1. Transformations
Section 2.7

2. Worksheets
“Transformations” introduces several transformations. Most of the functions we will deal with this semester are transformations of the functions discussed in “Library of functions”. These functions, such as y = x 2, y = x, and others, are called mother functions.
“Part II” of this worksheet summarizes the transformations for which you will be responsible.
“Transformations 2” and “Library of functions and transformations 2” provide more practice.

3. Intro to Transformations worksheet
Part I:
Graph carefully. Check your values with your neighbors often to make sure you are on the right track.
1. Complete the table and graph and x -3 -2 -1 1 2 3

4. Notice how for each x, the point is moved up 3 units to make h(x).-3 -2 -1 1 2 3 9 4 12 7
In the table, each h(x) value is 3 more than the corresponding f(x) value because we added 3 to each f(x).
Notice how for each x, the point is moved up 3 units to make h(x).

5. Transformations worksheet
Let c be a positive real number.
Transformation of graph
Number of question which is example
Vertical stretch by factor of c 5
Vert. compression by factor of c 6
Horizontal shift to right c units 4
Horizontal shift to left c units 3

6. Transformations worksheet cont.
Let c be a positive real number.
Transformation of graph
Number of question which is example
Vertical shift up c units 1
Vertical shift down c units 2
Reflection about x axis 7
Reflection about y axis 8

7. You can think through transformations by imagining what is happening to the y values.
For instance, if you compare
and , you’ll notice the second function’s y values are merely five times the first function’s y values. So each point is stretched away from the x-axis. The graph will be elongated. So we say the graph is vertically stretched by a factor of 5. Check it out by graphing both on your calculator!
2.7 homework: 1, 2, 3, 9, 10, 13, 14, 17, 18, 39, 41, 51, 65abc, 75, 89