1. Functions, Patterns and Proportional Relationships
Direct and Indirect Proportions

2. Function A function is like a machine
It has an input (x-value) and an output (y-value)
For every input, there is exactly ONE output
A function can be displayed by a rule, a table or graph.
Function Introduction Video

3. Function 1
y=5x - 1
Input
Rule
Output x
5x – 1 y -2 3 6

4. Function 2
y=-2x2
Input
Rule
Output x
-2x2 y -2 2 3 4

5. Can you find the pattern?
Input (x)
Output (y) 1 4 2 6 3 8 5
Complete the table
Can you write the function?

6. Graph the Function Y = x ÷ 4 Input Rule Output Ordered Pair X X ÷ 4 Y-4 2 4

7. Describing Functions X 1 2 3 4 y 9 18 27 36
“As x increases by 1, y increases by _____”

8. When one number increases, the other number also increases
Direct Proportion
Any function that can be written in the form y=kx, where K is a constant
EXAMPLE: y= 9x
When one number increases, the other number also increases X 1 2 3 4 y 9 18 27 36

9. Direct Proportion Example
David earns $15 each hour he works for his grandmother doing odd jobs around the house.
Fill in the table!
X (hours worked) 1 2 3 4
Y ($ made)

10. Direct Proportion Example
Now, write an equation!
X (hours worked) 1 2 3 4
Y ($ made)
$15
$30
$45
$60
Let x stand for the number of hours David worked and let y stand for the number of dollars she earns:
Y= ___ ___

11. Direct Proportion Y= 15x A direct proportion exists! $$ made
Hours worked

12. Direct Proportions in graphs
To determine whether a line is the graph of a direct proportion, follow this rule:
If a straight-line graph passes through the point (0,0), it is the graph of a direct proportion

13. Which line is the direct proportion?m

14. Indirect Proportion
When two numbers are multiplied and the answer is a constant (k)
EXAMPLE: xy=k
y= k x
For (1,8), xy = ______
For (2,4), xy = ______
For (4,2), xy = ______
For (8,1), xy = ______

15. Indirect Proportion

16. Is the function y=3x + 3 a direct proportion?
Thinking it Through
Is the function y=3x + 3 a direct proportion?

17. Thinking it Through Step 1: Pick a point If x = 1, y = ________
Is the function y=3x + 3 a direct proportion?
Step 1: Pick a point
If x = 1, y = ________
Y =
X _______

18. Thinking it Through Step 3: Pick another point If x=3, y= ___________
Is the function y=3x + 3 a direct proportion?
Step 3: Pick another point
If x=3, y= ___________
Y =
X _______

19. Thinking it Through Another Way:
Is the function y=3x + 3 a direct proportion?
Another Way:
Direct Proportions must pass through (0,0)
SO…when x=0, does y=0???

20. Hints for Proportion Questions
Numbers being multiplied??
It’s a Direct Proportion!
Numbers being divided??
It’s an Indirect Proportion!

21. Hints for Proportions Graph a straight line, going through (0,0)??
It’s a Direct Proportion!
Graph a curve??
It’s an Indirect Proportion!

22. Question 1 Which describes the equation y = 50/x ? Direct proportion
b. Indirect proportion
C. Neither

23. Question 2 Which statement describes the equation y = 10x ?
Direct proportion
Indirect proportion
Neither

24. Question 3
The Willy Wonka Factory can make 2,000 chocolate bars per hour. This means there is a direct proportion between the number of hours the factory is operating and _________________________________________________________.

25. Classwork
COACH
Pg.154
Pg.158
Pg.162