1. Function, Domain, Range,
Rita Korsunsky

2. Relations and Functions
A relation is a connection between 2 sets of numbers. For example, (x, y)
The x-values represent the domain, and the y-values represent the range.
x is the independent variable and y is the dependent variable.

3. Functions
Function- A correspondence that assigns to every element in set D EXACTLY one element in set R.
Set D = domain;
Set R = range.
A function
Not a function
D R 5 6 8 10 14 23
D R 5 6 8 10 14 23

4. Vertical Line Test
Not a function
Function

5. Representing Relations and Functions
When a relation is also a function (passes a vertical line test), we often use “special” notation.
For example,
The mapping would be:

6. Practice Problems (in class)
State the domain and range: {(3, 4) (1, 6) (2, 6)}
Determine whether this mapping represents a function.
Is this a function?

7. Example 1
Find a rule for the pairings given below. Write your rule in function notation.
If I multiply the x-coordinate by 3, I get the y-coordinate. My rule is:
domain
range

8. Example 2 Is it a function? Yes, it passes the vertical line test.
Find the domain and the range of this function

9. Example 3
Tell whether each graph is the graph of a function. If it is, give the domain and range of the function. 1 5 8 -2
Passes the vertical line test. Yes, function.

10. Example 4
Tell whether each graph is the graph of a function. Give the domain and range.
Passes the vertical line test. No, not function.

11. Example 5
Tell whether each graph is the graph of a function. If it is, give the domain and range of the function.
Passes the vertical line test. Yes, function.

12. Example 6

13. Special Functions
You should know what the graphs of each of these 5 special functions look like.

14. Special Functions

15. Greatest integer Function
For all real numbers, x, the greatest integer function returns the largest integer.

16. Practice Problems 4. For g(x)=2x-1 find g(3) and g(-2). Graph g(x).
5. If h(x)=2x over the domain {-3,1,4}, what is the range? Does –h(x)=h(-x)?
Range = {-6,2,8}, yes