1. 4.4 Graphing a Function Rule:
Continuous: is a function that is unbroken.
Discrete: is a function, graph composed of distinct, isolated points.

2. GOAL:

3. Graphing a Function Rule:
Whenever we are given a function rule-(equation) we must always create a table to obtain the ordered pairs (x, y) we must use to create the corresponding graph.
Ex:
Provide the graph that represents: f(x) = - 2x +1

4. 1. First create a table X Y= - 2x + 1 Ordered Pair - 2 -2 ( -2 ) + 1
(-2, 5) -1
-2 ( -1 ) + 1
(-1, 3)
-2 ( 0 ) + 1
(0, 1) 1
-2 ( 1 ) + 1
(1, -1) 2
-2 ( 2 ) + 1
(2, -3) 3

5. 2. Take the ordered pair column and create the scale for both, x and y axis
(-2, 5)
(-1, 3)
(0, 1)
(1, -1)
(2, -3)
X axis

6. 3. Plot the ordered pairs. Ordered Pair y axis (-2, 5) (-1, 3) (0, 1)
(1, -1)
(2, -3)
X axis

7. 4. Connect the ordered pairs.
y axis
Ordered Pair
(-2, 5)
(-1, 3)
(0, 1)
(1, -1)
(2, -3)
X axis

8. 5. Label the graph with the proper function.
y axis
Ordered Pair
(-2, 5)
(-1, 3)
(0, 1)
(1, -1)
(2, -3)
X axis
f(x) = -2x + 1

9. Real-World Problems:
The function rule W= 146c + 30,000 represents the total weight W, in pounds, of a concrete mixer truck that carries c cubic feet of concrete. If the capacity of the truck is about 200 ft3, What is a reasonable graph of the function rule?

10. Real-World Problems:
Create a table: C
W = 146c + 30,000
(c, W)
W = 146(0) + 30,000
(0, 30,000) 50
W = 146(50) + 30,000
(50, 37,300)
100
W = 146(100) + 30,000
(100, 44,600)
150
W = 146(150) + 30,000
(150, 51,900)
200
W = 146(200) + 30,000
(200, 59,200)

11. The graph does produce a line.
(c, W)
(0, 30,000)
(50, 37,300)
(100, 44,600)
(150, 51,900)
(200, 59,200)
Weight (lbs)
60,000
40,000
20,000 50
100
150
200
Concrete (ft3)
The graph does produce a line.
Continuous Graph.

12. YOU TRY IT:
A local cheese maker is making cheddar cheese to sell at a farmer’s market. The amount of milk used to make the cheese and the price at which he sells the cheese are shown. Write a function for each situation. Graph each function and decide if it is continuous or discrete.

13. Milk:
1. The weight w of cheese, in ounces, depends on the number of gallons m of milk used.

14. Cheese:
2. The amount a of money made from selling cheeses depends on the number n of wheels sold.

15. Cheese:
1.Looking at the data the rule is: w = 16m

16. Any amount of milk can be used so connect the points: Continuous.
Graph:
W = 16m m W 1 16 2 32 3 48 4 64 70 60
Weight, W 40 30 20 10 2 4 6 8 10
milk, m
Any amount of milk can be used so connect the points: Continuous.

17. Cheese:
2. Looking at the data the rule is: a = 9m

18. Amount of money, a Wheels sold, n
Graph:
a = 9n n a 1 9 2 18 3 27 4 36 35 30
Amount of money, a 25 20 15 10 5 2 4 6 8 10
Wheels sold, n
Since we only get that specific amount, we cannot connect the points: Discrete

19. YOU TRY IT:
The amount of water w in a wadding pool, in gallons, depends on the amount of three times the time t, in minutes, the wadding pool has been filling.

20. Pool:
2. Looking at the data the rule is: w = 3t

21. Any amount of water can be used so connect the points: Continuous.
Graph:
W = 3t t W 1 3 2 6 9 4 12 18 15
Water, w 12 9 6 3 2 4 6 8 10
minutes, t
Any amount of water can be used so connect the points: Continuous.

22. YOU TRY IT:
The cost C for baseball tickets, in dollars depends on the number n of tickets bought and each ticket is being sold for $16.

23. Baseball:
2. Looking at the data the rule is: C = 16n

24. Only that amount of money can be collected: Discrete.
Graph:
C= 16n n C 1 16 2 32 3 48 4 64 60 50
Cost, C 40 30 20 10 2 4 6 8 10
tickets, n
Only that amount of money can be collected: Discrete.

25. Graphing a Non-Linear Function Rule:
Whenever we are given a function rule-(equation) we must always create a table to obtain the ordered pairs (x, y) we must use to create the corresponding graph.
Ex:
Provide the graph that represents: f(x) = - x2 + 1

26. 1. First create a table X Y= - x2 + 1 Ordered Pair - 2 -( -2 ) 2 + 1
(-2, -3) -1
- ( -1 ) 2 + 1
(-1, 0)
- ( 0 ) 2 + 1
(0, 1) 1
-( 1 ) 2 + 1
(1, -0) 2
- ( 2 ) 2 + 1
(2, -3) 3

27. 2. Take the ordered pair column and create the scale for both, x and y axis
(-2, -3)
(-1, 0)
(0, 1)
(1, -0)
(2, -3)
X axis

28. 3. Plot the ordered pairs. Ordered Pair (-2, -3) y axis (-1, 0) (0, 1)
(1, -0)
(2, -3)
X axis

29. VIDEOS:
Functions

30. VIDEOS:
Functions

31. Problems: As many as it takes to master the concept.
CLASS WORK:
Pages: 257 – 259
Problems: As many as it takes to master the concept.