This document contains: 1. An outline for a mathematics course covering functions and their graphs, basic business mathematics, and logic. 2. Lessons on identifying functions from relations, evaluating functions, and representing real-life situations using functions including piecewise functions. 3. Examples of evaluating functions, operations on functions, and determining whether a relation is a function based on its graph or ordered pairs. 4. An activity drilling students on identifying functions versus non-functions.

1. a. Functions and their Graphs
b. Basic Business Mathematics
c. Logic
Liza L. Magalso
Mathematics G11
General Mathematics
Course Outline

2. Real-Life Functions
Piece-wise functions
Evaluation on functions
Liza L. Magalso
Mathematics G11
June 16, 2016
General
Mathematics
Functions

3. What we are about to learn…
identify functions from relations
evaluates a function
represents real-life situations
using functions, including piece-
wise functions

4. 4
2. 5 + -8 =
7
 Review: Operations on Functions
1. 3 + 4 =
3. -4 + -7 =
-3
-11
4. -2 + 8 = 6

5. 5
2. 6 - 8 =
3
 Review: Operations on Functions
1. 5 - 2 =
3. -4 - 3 =
-2
-7
4. 7 - -5 = 12

6. 6
2. (3) (-6) =
20
 Review: Operations on Functions
1. (5) (4) =
3. (-7) (4) =
-18
-28
4. (-5) (-3) =15

7. 7
2. 15 ÷ -3 =
5
 Review: Operations on Functions
1. 20 ÷ 4 =
3. -8 ÷ -2 =
-5
4
4. -30 ÷ 6 = -5

8. Functions
 Functions relate an input to an
output
Functions in real life:
Output: Score in the test
Input: No. of hours studied

9. Functions
Functions in real life:
 Give another real-life situations
involving functions

10. Functions
Illustration of Functions:
b. mapping or arrow diagram
a. set of ordered pair
c. graphing

11. Functions
a. set of ordered pair
1. {(3,2), (4,0), (5,1), (2,3)} Function
2. {(1,2), (0,3), (1,6), (5,4)}
3. {(3,4), (3,0), (3,1), (3,3)}
4. {(4,2), (3,2), (6,2), (5,2)}
Not Function
Not Function
Function

12. Functions
a. set of ordered pair ( x, y )
x - First element Domain
y - Second Element Range
Independent variable
Dependent variable

13. Functions
b. diagram
3
4
5
Function
One-to-One
Relation
a
b
c
2
3
6
9
4
3
2
3
6
2
3
6
2
3
Function Not Function Not Function
Many-to-One
Relation
One-to-Many
Relation
Not all elements
are represented

14. Functions
c. graphing

15. Functions
c. graphing

16. 16
Function
s
Evaluation on Functions

17. Functions
Evaluation on Functions
h(-3) = (-3)2
-4(-3) + 9
= 9 + 12 + 9
= 30

18. Piece-wise Functions
 Functions in pieces

19. Piece-wise Functions

20. Piece-wise Functions

21. Piece-wise Functions

22. Functions
Answer Me:
Is this relation a function?
1. {(1,3),(2,3),(3,3)}
2. {(2,3),(2,3),(4,3)}
3. {(-3,3),(-2,3),(-
5,3)}
4. {(1,4),(2,4),(3,4)}
Yes
No
Yes
Yes

23. Functions
Answer Me:
Is this relation a function?
YesNo

24. Functions
Answer Me:
Is this graph a function?
YesNo

25. Functions
Answer Me:
Is this graph a function?

26. Functions
Answer Me:
Find the value:
1. f(x) = 3x2
- 4x +
9
x = 0, x = -2
2. h(x) = 4x3
- 6x -
12
3. g(x) = 5x + 4
4. f(x) = x2
+ 5x
f(0) =
9
f(-2) =
29
h(0) =
-12
f(0) =
0
g(0) = 4
h(-2) = 32
g(-2) =
-6
f(-2) =
-6

27. Activity: Group Drill
• Function: (Oh
Yes!)
• Not Function: (Oh
No!)
1. {(-2,3),(2,3),(-3,3)}
2. {(3,3),(2,2),(4,4)}
3. {(1,8),(1,5),(1,3)}
4. {(7,3),(8,3),(5,3)}
Oh Yes!
Oh Yes!
Oh No!
Oh Yes!

28. Activity: Group Drill
• Function: (Oh Yes!) • Not Function: (Oh No!)
Oh Yes!
Oh No!Oh Yes!
Oh No!

29. Activity: Group Drill
• Function: (Oh Yes!) • Not Function: (Oh
No!)
Oh Yes! Oh No! Oh Yes!Oh No!

30. Activity: Group Drill
• Function: (Oh Yes!) • Not Function: (Oh No!)
Oh Yes!
Oh No!Oh Yes!
Oh No!

31. Functions
Find my value:
1. f(x) = 2x2
- 3x + 4 ,
f(0)?
2. h(x) = x3
- 3x - 3 ,
h(-2)
3. g(x) = 6x - 4 ,
g(3)
4. f(x) = 5x2
+ 3x - 6, f(-
3)
f(0) = 4
h(-2) = -5
g(3) =
14
f(-3) = 30

32. Functions
Assessment:
A. Which of the following are functions
1. {(4,3),(-4,3),(3,3)}
2. {(2,5),(4,4),(2,3)}
Function
Not Function
Not FunctionFunction
3. 4
.

33. Functions
Assessment:
B. Evaluate the following:
1. f(z) = z2
- 5z + 2
2. h(x) = 3x - 4
4
f(-2) = 16f(-2)
3. g(x) = 2x3
+ 3x - 1
4. f(x) = x4
+ 6x3
-3
f(0)
f(-3)
f(-1)
f(-0) = -1
f(-3) = -64
f(-1) = -8

34. Assignment:
A. Find the following:
g(x) = x + 1 f(x) = x - 1
1. (g + f) (x)
5. (g f) (x)2. (g - f) (x)
4. (g ÷ f) (x)
3. (gf) (x)

35. Thank you!!!