1. Warm up Find f(-3). 4 Find g(0).
Given r(x) = 2x – 1, evaluate the domain {0, 1, 2, 3}. What is the range of r(x)? 4 -2
Range: {-1, 1, 3, 5}

2. Even and Odd Functions
The easiest thing to do is to plug in 1 and -1 (or 2 and -2)
if you get the same y, then it’s Even.
If you get the opposite y, then it’s Odd.
If you get different y’s, then it’s Neither.

3. Algebraically A function is even if A function is odd if
All of the exponents of the variable are even.
A function is odd if
All of the exponents of the variable are odd.
The easiest thing to do is to plug in 1 and -1 (or 2 and -2)
if you get the same y, then it’s Even.
If you get the opposite y, then it’s Odd.
If you get different y’s, then it’s Neither.
A function is neither if
The exponents are a mixture of odd and even

4. All constants really have a x0
BEWARE OF CONSTANTS
All constants really have a x0
The easiest thing to do is to plug in 1 and -1 (or 2 and -2)
if you get the same y, then it’s Even.
If you get the opposite y, then it’s Odd.
If you get different y’s, then it’s Neither.

5. x0 is EVEN!!
The easiest thing to do is to plug in 1 and -1 (or 2 and -2)
if you get the same y, then it’s Even.
If you get the opposite y, then it’s Odd.
If you get different y’s, then it’s Neither.

6. Even, Odd or Neither?
Ex. 1
Algebraically 1
ODD

7. Even, Odd or Neither?
Ex. 2
Algebraically x0
EVEN

8. Even, Odd or Neither? 1 x0
EVEN
ODD

9. Even, Odd or Neither? x0
ODD
ODD
Even

10. Even, Odd or Neither? 1
1 x0
neither
ODD
neither

11. Graphically A function is even if A function is odd if
The graph reflects across the y-axis
(means you can fold it hotdog style and it would match up).
A function is odd if
The easiest thing to do is to plug in 1 and -1 (or 2 and -2)
if you get the same y, then it’s Even.
If you get the opposite y, then it’s Odd.
If you get different y’s, then it’s Neither.
The graph has 180 rotational symmetry about the ORIGIN
(means you could turn it upside-down & it would still look the same...it must go through the origin).

12. Even, Odd or Neither?
Ex. 3
Graphically
EVEN

13. Even, Odd or Neither?
Ex. 4
Graphically
Neither 

14. Even, Odd or Neither? 
EVEN
ODD

15. Even, Odd or Neither?  
EVEN
Neither
ODD

16. If the dots shown are part of an even function, what points are also on the function?

17. If the dots shown are part of an odd function, what points are also on the function?

19. Intersections of graphs

20. Points of Intersection

21. Points of Intersection
Graphically and Algebraically
The easiest thing to do is to plug in 1 and -1 (or 2 and -2)
if you get the same y, then it’s Even.
If you get the opposite y, then it’s Odd.
If you get different y’s, then it’s Neither.

22. Algebraically Set the equations equal to each other Solve for x
Substitute in to either equation to find y
Write answer as ordered pair

23. Find the point of intersection.

24. Find the point of intersection.

25. Find the point of intersection.

26. Find the point of intersection.

27. Graphically Graph the equations on 1 coordinate plane
Find where the graphs intersect
Write answer as an ordered pair

28. 5. Find the point of intersection.

29. 6. Find the point of intersection.

30. 7. Find the point of intersection.

31. 8. Find the point of intersection.

32. 9. Find the point of intersection.

33. CW/HW Worksheet