4.4 Graphing a Function Rule:
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Transcript of 4.4 Graphing a Function Rule:
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.