For the given relation: (1, 4), (3, 7) (5, 11), (7, 11) Do Now 5 - ¾ = 2. ⅘ + ¼ = 3. 12 ÷ 0.04 = 4. 300x0.03 = For the given relation: (1, 4), (3, 7) (5, 11), (7, 11) 5. Is it a function? 6. State the domain and range.

Review In a group of three of four, do the following on a white board when I instruct you to do so. Graph a function Draw a graph that isn’t a function Create a mapping that represents a function Create a mapping the doesn’t represent a function State the domain of the mapping from the non-function State the range of your non-function Develop a context (story) for your data. What’s the relationship between the ordered pairs? Be able to explain.

3.3 Modeling with Functions In this lesson, you will be able to Identify the independent and dependent variables of a function Convert to function notation Create a function based on a word problem and be able to use it to find solutions

What’s Are Independent and Dependent Variables? The independent variable is the number you get to choose. It’s the ingredients you choose for your sausage. The dependent variable is what pops out of the function. Its existence depends on the independent variable. It’s the sausage. The sausage is going to dependent on what you put inside the sausage machine.

Let’s Try This Here’s a story. Let’s identify the dependent and independent variables. In the winter, more electricity is used when the outside temperature goes down, and less is used when the outside temperature rises. What depends on what? Dependent: Independent:

We’re not done with these (in groups) The cost of shipping a package is based on the weight. What depends on what? Dependent: Independent: B. The faster Tom walks, the quicker he gets home.

Definition: Function Notation Instead of writing y = x + 4, you can replace y with f(x). We say “F of X”. It’s the same as y, it’s just another way to write it. Let’s try this out by writing an equation in function notation. Amanda babysits and charges $5 per hour.

Example A lawyer’s fee is $180 per hour for his services. How much does the lawyer charge for 5 hours? Independent: Dependent: Function: Answer:

Your Try in Group The admission fee at a carnival is $9. Each ride costs $1.75. How much does it cost to go to the carnival and then go on 12 rides? Independent: Dependent: Function: Answer:

You Try Individually Kate earns $7.50 per hour. How much money will she earn after working 8 hours? Independent: Dependent: Function: Answer:

How Does Domain and Range Fit Into This? When a function describes a real-world situation, every real number is not always a reasonable choice for the domain and range. For example, a number representing the length of an object cannot be negative, and only whole numbers can represent a number of people. Let’s see how this works. Manuel has already sold $20 worth of tickets to the school play. He has 4 tickets left to sell at $2.50 per ticket. Write a function for the total amount collected from ticket sales. Function: Domain: Range:

You Try In Groups A telephone company charges $0.25 per minute for the first 5 minutes of a call plus a $0.45 connection fee per call. Write a function for the total cost in dollars of making a call. Function: Domain: Range:

You Try Individually The temperature early in the morning is 17 °C. The temperature increases by 2 °C for every hour for the next 5 hours. Write a function for the temperature in degrees Celsius. Function: Domain: Range: 2. Joe earns $8.50 per hour proofreading advertisements at a local newspaper. He works no more than 5 hours a day. Write a function for his earnings. 3. Charles will babysit for up to 4 hours and charges $7 per hour.

Wrapping It Up Write 3x + 2y = 12 in function notation? How would you do it? 2. Identify the dependent and independent variables in each situation. A. The total cost of running a business is based on its expenses. B. The price of a house depends on its area. C. The time it takes you to run a certain distance depends on the distance. D. The number of items in a carton depends on the size of the carton.

HW 3.3. P. 132 #3-23 ALL