1. Pre-Calculus Lesson 3: Translations of Function Graphs Vertical and horizontal shifts in graphs of various functions

2. The Absolute Value Function What does the graph of y = |x| look like?

3. y =|x| y x 10 -10

4. y =|x|+3 y x 10 -10

5. y =|x|+3 y x 10 -10

6. y =|x|-3 y x 10 -10

7. y =|x|-3 y x 10 -10

8. Observation #1: Adding to or subtracting from a function will shift the graph of the parent function up or down, respectively.

9. y =|x+3| y x 10 -10

10. y =|x+3| y x 10 -10

11. y =|x-3| y x 10 -10

12. y =|x-3| y x 10 -10

13. Observation #2: Adding to or subtracting from the variable will shift the graph of the parent function left or right, respectively.

14. y =-|x| y x 10 -10

15. y =-|x| y x 10 -10

16. http://www.uiowa.edu/~examserv/mathmatters/tutorial_quiz/geometry/typesofsymmetry_clip_image017.gif f(x) f(-x)

17. Observation #3: Negating the function will reflect the parent function over the x-axis. Negating the variable will reflect the parent function over the y-axis.

18. Even and Odd Functions  An even function is:  Symmetric with respect to the ______________.  Defined by the equation ______________.  An odd function is:  Symmetric with respect to the ______________.  Defined by the equation ______________.

19. Even and Odd Functions  An even function is:  Symmetric with respect to the ______________.  Defined by the equation ______________.  An odd function is:  Symmetric with respect to the ______________.  Defined by the equation ______________. y-axis

20. Even and Odd Functions  An even function is:  Symmetric with respect to the ______________.  Defined by the equation ______________.  An odd function is:  Symmetric with respect to the ______________.  Defined by the equation ______________. y-axis

21. Even and Odd Functions  An even function is:  Symmetric with respect to the ______________.  Defined by the equation ______________.  An odd function is:  Symmetric with respect to the ______________.  Defined by the equation ______________. y-axisorigin

22. Even and Odd Functions  An even function is:  Symmetric with respect to the ______________.  Defined by the equation ______________.  An odd function is:  Symmetric with respect to the ______________.  Defined by the equation ______________. y-axisorigin

23. Determine whether each function is even, odd, or neither.

35. Practice Describe the shifts in the graph of the function from the parent function of. State the coordinates of the vertex point of the graph. Determine if the function is odd, even, or neither and justify your answer.