1. Unit 2: Transformations of functions
Final Exam Review

2. Topics to cover Transformations of Functions Characteristic Points
Factoring
Simplifying Radicals

3. Transformations of functions
You can move a function anywhere on a graph using transformations
You can go:
UP AND DOWN
LEFT AND RIGHT
STRETCH AND SHRINK
REFLECT OVER THE X AXIS AND Y AXIS

4. Transformations UP AND DOWN
Use these rules when translating a function up and down
Up:
f(x) + c
Example: y = f(x) + 4 will move a function Up 4
Down:
f(x) – c
Example: y = f(x) – 5 will move a function Down 5

5. Transformations left and right
Use these rules when translating a function left and right
Left:
f(x + c)
Example: y = f(x + 2) will move a function Left 4
Right:
f(x – c)
Example: y = f(x – 6) will move a function Right 6

6. Stretch and Shrink Use these rules when stretching and shrinking
c ∙ f(x) when c > 1
Example: y = 3 f(x) will stretch a function by 3
Shrink:
c ∙ f(x) when 0 < c < 1
Example: y = 𝟐 𝟑 f(x) will shrink a function by 𝟐 𝟑

7. Reflections over the x axis and y axis
Use these rules when reflecting a functions over the x axis or the y axis
X axis:
-f(x)
The negative is OUTSIDE of the function
Y axis:
f(-x)
The negative is INSIDE of the parenthesis with the x

8. Given the function, write the transformations
Example
y = 5 f(x – 3)
y = -f(x) + 2
y = 1 3 f(−x+7) - 8
Answers
Stretch 5, Right 3
Reflect over the X axis, Up 2
Shrink 𝟏 𝟑 , Reflect over the y axis, Left 7, Down 8

9. Given the function, write the transformations
Now you try:
y = f(x – 4) – 3
y = 6 f(x + 2)
y = − 1 3 f(x) + 6

10. Given the transformations, write the equation
Example
Left 1, Up 9
Shrink , Reflect over the x axis
Stretch 10, Right 4, Down 2
Answers
y = f(x + 1) + 9
y = - 𝟑 𝟒 f(x)
y = 10 f(x – 4) – 2

11. Given the transformations, write the equation
Now you try:
Right 7, Reflect over the y axis
Stretch 4, Left 2, Down 5
Reflect over the x axis, Shrink 4 5 , Up 8

12. CHARACTERISTIC points
When transforming points, you must figure out:
If the transformation is affecting the X VALUE or the Y VALUE
Then ADD, SUBTRACT, or MULTIPLY the point by the correct value
UP AND DOWN will affect the y value
LEFT AND RIGHT will affect the x value
STRETCHING AND SHRINKING will affect the y value

13. CHARACTERISTIC points
Example
Move the point (5, -2) using the transformations in the function y = f(x – 4)
Answer: (9, -2)
*This transformation moves the function right 4, so the x value is moved right 4 spaces

14. CHARACTERISTIC points
Now you try:
Move the point (-4, 2) using the functions:
y = f(x) – 5
y = f(x + 1)
y = 3 f(x)
y = f(x – 2) + 9

15. FACTORING
Factoring helps you to find where a function crosses the X AXIS
Steps to follow when factoring
Draw an X
For the number on the top of the X, MULTIPLY the FIRST number by the LAST number
For the number on the bottom of the X, write the MIDDLE number
Figure out which 2 numbers will MULTIPLY to get the top number on the X and ADD to get the bottom number on the X and use reverse Xbox method, or:
SPLIT THE MIDDLE by rewriting your equation with the 2 numbers that you found on the X.
Group the FIRST 2 TERMS and the LAST 2 TERMS.
Take out the GCF of the first 2 terms and the last 2 terms
Use your GCF and what was left over to write your equation in factored form

16. FACTORING
Watch this Video for an example

17. FACTORING
Try this one now:
Factor 6x2 – 13x + 2

18. Simplifying Radicals
Simplifying Radicals is necessary in math in order to simplify your answer COMPLETELY
Steps to Follow:
Break down the number under the radical using a FACTOR TREE
CIRCLE any pairs of numbers
The numbers that have a PAIR can be taken out of the radical and put on the OUTSIDE
If there is more than one pair, MULTIPLY the numbers on the outside of the radical
Write what is left over without a pair UNDER the radical symbol

19. Simplifying Radicals
Now try this one:
135

20. ALL DONE