1. Section 1.2 Basics of Functions

2. Definition of a Relation
Math Section 1.2
Definition of a Relation
A relation can be expressed as a set of ordered pairs. The domain of a relation is the set of first elements in the ordered pairs, and the range is the set of second elements.
Relation: {(0 , 5), (2 , 1), (2 , 1), (3 , 8)}
Domain: {0, 2, 3}
Range: {5, 1, 1, 8}
Relation: {(0 , 5), (2 , 1), (2 , 1), (3 , 8)}
Domain: {0, 2, 3}
Relation: {(0 , 5), (2 , 1), (2 , 1), (3 , 8)}

3. Example
Find the domain and the range.

4. Definition of a Function
Math Section 1.2
Definition of a Function
A function is a relation for which each element of the domain corresponds to exactly one element of the range.
Relation: {(0 , 5), (2 , 1), (2 , 1), (3 , 8)} Function: {(0 , 2), (1 , 8), (5 , 2), (1 , 3)}
In other words, no x coordinate can be paired with more than one y coordinate.
1 8 

5. Example
Determine whether each relation is a function?

6. Function Notation

7. A function can also be expressed as an equation.
Math Section 1.2
Function Notation
A function can also be expressed as an equation.
f(x) = x2 + 5x  2
“f of x”
f(3) = (3)  2 = 22
f(1) = (1)2 + 5(1)  2 = 6
f(z+2) = (z+2)2 + 5(z+2)  2
= z2 + 4z z + 10  2
= z2 + 9z + 12

8. Example
Evaluate each of the following.

9. Example
Evaluate each of the following.

10. Example
Evaluate each of the following.

11. Graphs of Functions

12. x f(x)=-2x (x,y) g(x)=-2x+3 -2 f(-2)=4 (-2,4) g(-2)=7 (-2,7) -1
(-1,2)
g(-1)=5
(-1,5)
f(0)=0
(0,0)
g(0)=3
(0,3) 1
f(1)=-2
(1,-2)
g(1)=1
(1,1) 2
f(2)=-4
(2,-4)
g(2)=-1
(2,-1)
See the next slide.

13. g(x)
f(x)

14. Example
Graph the following functions f(x)=3x-1 and g(x)=3x

15. The Vertical Line Test

16. The first graph is a function, the second is not.

17. Example
Use the vertical line test to identify graphs in which y is a function of x.

18. Example
Use the vertical line test to identify graphs in which y is a function of x.

19. Obtaining Information from Graphs

20. Example
Analyze the graph.

21. Identifying Domain and Range from a Function’s Graph

22. Math Section 1.2
The domain of a function is the set of all x values for which the function is defined.
Domain
x2  4  0
x  2, 2
( , 2)  (2 , 2)  (2 , )
Domain
2x + 6  0
2x  6
x  3
[3 , )

23. Math 112 Section 1.2 Finding the Domain & Range of a Function
The domain of a function is the set of all x values from the graph.
The range of a function is the set of all y values from the graph.
Domain: ( , )
Range: [1 , )

25. Example
Identify the Domain and Range from the graph.

26. Example
Identify the Domain and Range from the graph.

27. Example
Identify the Domain and Range from the graph.

28. Identifying Intercepts from a Function’s Graph

29. Example
Find the x intercept(s). Find f(-4)

30. Example
Find the y intercept. Find f(2)

31. Example
Find the x and y intercepts. Find f(5).

32. Find f(7).

33. Find the Domain and Range.

35. Example
Determine whether each equation defines y as a function of x.