Modeling Using Function Notation Presented by Mr Laws

Modeling Using Function Notation Presented by Mr. Laws Math I, JCMS

Standard/Goal • FIF. 1 - Understand the concept of a function and use function notation. • Build an understanding that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range by recognizing that: o If f is a function and x is an element of its domain, the f(x) denotes the output of f corresponding to the input x. o The graph of f is the graph of the equation y = f(x). • FIF. 2 – Use function notation to evaluate linear, quadratic, and expontential functions for inputs in their domain, and interpret statements that use function notation in terms of a context.

Target Statements • I can write and interpret function notations by using a model and identifying independent and dependent variables. • I can write a function in a real-world situation by creating a reasonable choice for the domain and range.

Identifying the Independent and Dependent Variables 1. The value of the dependent variable (y)depends on, or is a function of, the value of the independent variable (x). 2. If x is the independent variable, and y is the dependent variable, the function notation will read y = f(x).

Identifying the Independent and Dependent Variable. • Example #1: A lawyer fee is $180. 00 per hour for his services. How much does the lawyer charge for 5 hours? a. Describe the relationship between the lawyer’s fee and the hours he works. Answer: The fee of the lawyer depends on how many hours he works b. What is the Dependent and Independent variable? Answer: Dependent: fee; Independent: hours; let (h) represent the hours the lawyer works. c. Write a function notation for the lawyer’s fee. Answer: f(h) = 180 h d. How much does the lawyer charges for 5 hours? Answer: f(5) = 180(5) f(5) = $900

Practice#1 Identifying the Independent and Dependent Variable. • Problem # 1: 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? a. Describe the relationship within this scenario. b. What is the Dependent and Independent variable? c. Write a function notation. d. How much does it cost to go to the carnival and then go on 12 rides?

Choosing a Reasonable Domain and Range 3. When a function describes a real-world situation, every real number is not always a reasonable choice for the domain and range. o For example: A number representing the length of an object cannot be negative, and only whole numbers can represent people.

Finding a Reasonable Domain and Range. • Example # 2: 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. • Step 1. Create a variable for the unknown. Let (t) represent the number of tickets; f(t)= total amount collected from ticket sales. • Step 2. Write a function rule based on the provided information. f(t) = 2. 5 t + 20 • Step 3. Identify a reasonable domain based on the tickets left to sell. 4 tickets left; reasonable domain is {0, 1, 2, 3, 4) • Step 4. Substitute the values into the function rule to find the range. The range is {$20, $22. 50, $25, $27. 50, $30}

Practice#2 Finding a Reasonable Domain and Range. • Problem # 2: Tammy earns $8. 50 per hour proofreading advertisements at a local newspaper. She works no more 5 hours a day. Write a function for the total number of hours she works. • Step 1. Create a variable for the unknown. • Step 2. Write a function rule based on the provided information. • Step 3. Identify a reasonable domain based on the information provided • Step 4. Substitute the values into the function rule to find the range.

Summary Ø Are you capable of doing the target statements given at the beginning of this lesson? Explain Ø What are some important things to remember about this lesson? Ø Do you have additional questions pertaining to this lesson?