The document covers various mathematical concepts including evaluating the function f(x)=5x-3, graphing points, and understanding relations and functions. It explains the definitions of domain and range, types of relations (discrete and continuous), and provides examples to illustrate each concept. Additionally, it poses questions regarding the classification of given sets of points and their properties.

1. a) Evaluate f(x)= 5x-3 for x=4
a) Graph the following point on a graph. *Label Each*
(1, 3), (-1, 0), (1/2, -4), (0, 4)

2. a) Solve for y: f(x)= 5x-3 for x=4
f(4)= 5(4)-3
f(4)=20-3
f(4)=17
b) Graph the following point on a graph. *Label Each*
(1, 3), (-1, 0), (1/2, -4), (0, 4)
(1, 3)
(-1, 0)
(0, 4)
(1/2, -4)

3. Relations
 What is a relationship?
 In math a relation is a connection between a set of
inputs and a set of outputs
Review on Relations and Functions

4. Representations
(other than equations)
1) Ordered pairs:
(-3, -2), (5, 0), (0, 1), (-1, 4), (4, 5), (2, -5)
2) Table:
x -3 -1 0 2 4 5
y -2 4 1 -5 5 0

5. 3) Graph
(-3, -2)
(5, 0)
(0, 1)
(-1, 4)
(4, 5)
(2, -5)

6. 4) Mapping
(-3, -2), (5, 0), (0, 1), (-1, 4), (4, 5), (2, -5)
-
3
-
1
5
2 4
0
-
5
-
2
0 1 4 5

7. 4) Mapping (another way)
(-3, -2), (5, 0), (0, 1), (-1, 4), (4, 5), (2, -5)
-3
-1
0
2
4
5
-5
-2
0
1
4
5

8. Domain and Range
 Domain- All inputs
 Range- All outputs
(-3, -2), (5, 0), (0, 1), (-1, 4), (4, 5), (2, -5)
Domain: -3, 5, 0, -1, 4, -5
Range: -5, -2, 0, 1, 4, 5

9. Function
 A function is a special kind of relation where
every input goes to exactly one output
 It’s PREDICTABLE!
*Can be written using Function Notation:

10. One-to-one
 Every input has a unique output

11. Onto
• Every output has an input

12. Discrete vs. Continuous
 Discrete relation: A relation where the
domain is a set of individual points
 Continuous relation: A relation that can
be graphed with a line or smooth curve

13. Domain?
Range?
Function?
One to one?
Onto?
Discrete or Continuous?

14. {(2,3), (3,4), (5,1), (6,2), (2,4)}
Domain?
Range?
Function?
One to one?
Onto?
Discrete or Continuous?

15. Domain?
Range?
Function?
One to one?
Onto?
Discrete or Continuous?

16. Domain?
Range?
Function?
One to one?
Onto?
Discrete or Continuous?

17. Domain?
Range?
Function?
One to one?
Onto?
Discrete or Continuous?

18. Domain?
Range?
Function?
One to one?
Onto?
Discrete or Continuous?

19. {(2,3), (3,4), (5,1), (6,2), (3,3)}
Domain?
Range?
Function?
One to one?
Onto?
Discrete or Continuous?

20. Domain?
Range?
Function?
One to one?
Onto?
Discrete or Continuous?

21. Domain?
Range?
Function?
One to one?
Onto?
Discrete or Continuous?

22. Domain?
Range?
Function?
One to one?
Onto?
Discrete or Continuous?

23. Domain?
Range?
Function?
One to one?
Onto?
Discrete or Continuous?

24. The number of employees a company had in each year from 2004 to 2009
were 25, 28, 34, 31, 27, and 29.
Domain?
Range?
Function?
One to one?
Onto?
Discrete or Continuous?

25. Domain?
Range?
Function?
One to one?
Onto?
Discrete or Continuous?

26. Domain?
Range?
Function?
One to one?
Onto?
Discrete or Continuous?

27. Domain?
Range?
Function?
One to one?
Onto?
Discrete or Continuous?