1. Introduction to Functions
Mathematical Functions 1

2. Remember Me … remember Me
Psst … my previous name was ‘y’

3. Example

4. Key Terms
Function – A pairing of two sets of numbers. The first set of numbers is paired with exactly one element of the second set.
Say huh????? ….. otra vez 4

5. This is a function:
Each input has one output

6. Function take three….. 2 3 5 4 1 10 2 3 5 4 1 10 2 6 7 2 6 7 input
output 2 3 5 4 1 10
input
output 2 6 7 2 6 7

7. Some inputs have more than one output
This is not a function:
Some inputs have more than one output 5 7 9 2 3
input
output 2 3 5 7 9

8. Examples Determine if a set of ordered pairs represents a function:
{(3,4), (3,6), (5, 14), (7, 4)}
Not a function – An input of 3 gives 2 different outputs.
{(4,12), (3, 7), (5, 2), (3, 7), (8, 12)}
Is a function – Each input has one and only one output. 8

9. Function Machine
input
output

10. Function
input
output

11. Function
input
output

12. NOT
input
output

13. NOT a function Stop …. Lets practice Function 1. 2. 2 3 9 4 5 7 9 2.2
input
output 2.
2.2 26 3 2 9
NOT a function

14. Key Terms
Domain – The first coordinate in a set of ordered pairs. Known as the 'x' value, the input, left to right on the graph.
Range – The second coordinate in a set of ordered pairs. Known as the 'y' value, the output, top to bottom on the graph 14

15. Function Machine
input
output x
Domain
independent y
Range
dependent

16. Domain
All real values for x x

17. Range
All real values for y y

18. Example 1 Identify the domain and range of the function.
Input (pounds)
1.5
2.3
3.1
4.2
Output (dollars)
$7.80
$11.96
$16.12
$21.82

19. Now try guided practice 1-3, p. 7.
Answer
Domain:
1.5, 2.3, 3.1, 4.2
Range:
7.80, 11.96, 16.12, 21.82
Now try guided practice 1-3, p. 7.

20. Example 2
The domain of the function y = x-3 is 2, 5, 8, and 11. make a table for the function, then identify the range of the function.

21. Work on Guided Practice 4 and 5, p. 8.
Answer X 2 5 8 11
Y = x-3
2-3 = -1
5-3 = 2
8-3 = 5
11-3 = 8
Work on Guided Practice 4 and 5, p. 8.

22. Example 3
Write a rule for the function
Input 3 6 7 10
Output 15 30 35 50
Hint: Look at what is being done to the input values in order to achieve the outputs values.

23. Try Guided Practice 6 and 7, p. 8.
Answer
The input values are multiplied by 2 in order to get the output values.
Let
Input = x
Output = y
Therefore:
y = 5x
Try Guided Practice 6 and 7, p. 8.

24. Examples T = time C = cost c = 5t + 10
The table below shows the amount that a company charges for raft rental for up to 10 hours. Find an equation to represent the function. List the domain and range values.
T = time
C = cost
c = 5t + 10
Domain = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Range =
{15, 20, 25, 30, 35, 40, 45, 50, 55, 60} 24

25. Assignment