4.4 Graphing a Function Rule:Continuous: is a function that is unbroken.

Discrete: is a function, graph composed of distinct, isolated points.

GOAL:

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

1. First create a table

X Y= - 2x + 1 Ordered Pair

- 2 -2 ( -2 ) + 1 (-2, 5)-1 -2 ( -1 ) + 1 (-1, 3)0 -2 ( 0 ) + 1 (0, 1)1 -2 ( 1 ) + 1 (1, -1)2 -2 ( 2 ) + 1 (2, -3)3

2. Take the ordered pair column and create the scale for both, x and y axis

Ordered Pair

(-2, 5)(-1, 3)(0, 1)(1, -1)(2, -3)

X axis

y axis

3. Plot the ordered pairs.

Ordered Pair

(-2, 5)(-1, 3)(0, 1)(1, -1)(2, -3)

X axis

y axis

4. Connect the ordered pairs.

Ordered Pair

(-2, 5)(-1, 3)(0, 1)(1, -1)(2, -3)

X axis

y axis

5. Label the graph with the proper function.

Ordered Pair

(-2, 5)(-1, 3)(0, 1)(1, -1)(2, -3)

X axis

y axis

f(x) = -2x + 1

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?

Real-World Problems: Create a table:

C W = 146c + 30,000 (c, W)

0 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)

Graph:W

eigh

t (lb

s)

Concrete (ft3)The graph does produce a line.

Continuous Graph.

20,000

40,000

60,000

50 150100 200

(c, W)

(0, 30,000)

(50, 37,300)

(100, 44,600)

(150, 51,900)

(200, 59,200)

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.

Milk:

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

Cheese:

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

Cheese:

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

Graph:W

eigh

t, W

milk, mAny amount of milk can be used so connect the points: Continuous.

10

20

30

2 6 104 8

W = 16m m W

0 01 162 323 484 64

40

60

70

Cheese:

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

Graph:Am

ount

of m

oney

, a

Wheels sold, nSince we only get that specific amount, we cannot connect the points: Discrete

5

10

15

2 6 104 8

a = 9nn a

0 01 92 183 274 36

20

25

30

35

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.

Pool:

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

Graph:W

ater

, w

minutes, tAny amount of water can be used so connect the points: Continuous.

3

6

9

2 6 104 8

W = 3t t W

0 01 32 63 94 12

12

15

18

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.

Baseball:

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

Graph:Co

st, C

tickets, nOnly that amount of money can be collected: Discrete.

10

20

30

2 6 104 8

C= 16n n C

0 01 162 323 484 64

40

50

60

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

1. First create a table

X Y= - x2 + 1 Ordered Pair

- 2 -( -2 ) 2 + 1 (-2, -3)-1 - ( -1 ) 2 + 1 (-1, 0)0 - ( 0 ) 2 + 1 (0, 1)1 -( 1 ) 2 + 1 (1, -0)2 - ( 2 ) 2 + 1 (2, -3)3

2. Take the ordered pair column and create the scale for both, x and y axis

X axis

y axis Ordered Pair

(-2, -3)(-1, 0)(0, 1)(1, -0)(2, -3)

3. Plot the ordered pairs.

X axis

y axis Ordered Pair

(-2, -3)(-1, 0)(0, 1)(1, -0)(2, -3)

VIDEOS: Functions

https://www.khanacademy.org/math/trigonometry/functions_and_graphs/function_introduction/v/basic-linear-function

https://www.khanacademy.org/math/trigonometry/functions_and_graphs/function_introduction/v/what-is-a-function

VIDEOS: Functions

https://www.khanacademy.org/math/trigonometry/functions_and_graphs/function_introduction/v/functions-as-graphs

CLASS WORK:

Pages: 257 – 259

Problems: As many as it takes to master the concept.