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

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

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

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

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) 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)

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.

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

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.

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

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

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

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.

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

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.

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

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

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

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

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.