Lesson 1.6 Represent Functions as Rules and Tables Essential Question: How do you represent functions as tables and rules?

Before we start… ITunes is having a major sale on music right now. Songs cost $0.50 each! What is your cost if you buy… 4 songs? 8 songs? 12 songs? 20 songs? Do you notice a pattern?

What is a relation? A set of ordered pairs Relates an input and an output

What is an… input? the x values output? the y values

What is a function? A special relation Each input has exactly one output Each x has one y

Functions The most useful mathematical idea for modeling the real world. In nearly every physical phenomenon we observe that one quantity depends on another. Functions describe the dependence of one quantity on another.

Real World Examples Height is a function of age Temperature is a function of date Cost of mailing a package is a function of weight Number of bacteria in a culture is a function of time

How does a function work? You plug the input in and follow the rule to get your output.

What are domain and range? The numbers you plug into the function (the x’s) The answers you get after performing a function (the y’s) x 1 2 3 4 y 5 10 15 20 𝑦=5𝑥

The input-output table shows the cost of various amounts of regular unleaded gas from the same pump. Identify the domain and range of the function. Input (gallons) 10 12 13 17 Output (dollars) 19.99 23.99 25.99 33.98

Identify the domain and range of the function. Input 1 2 4 Output 5

Identify the domain and range Input Output 5 1 7 2 15 3 44

Identify domain and range

Identify domain and range Input Output 6 5 12 7 21 10 42 17

Mapping Diagrams A function may be represented by a mapping diagram. An output may be paired with more than one input, but no input is paired with more than one output.

How do I identify a function? Each input will have only ONE output. Mapping diagrams, tables, and ordered pairs can be used to identify a function.

Tell whether the pairing is a function

Tell whether the pairing is a function

Tell whether the relation is a function. Input 9 25 Output 3 -3 5 -5 Input -4 4 8 Output 32

Tell whether the relation is a function. Input 3 6 9 12 Output 1 2 Input 2 4 7 Output 1 3

Tell whether the relation is a function. 0,2 , 1,4 , 2,6 , 3,8 −2,4 , 2,4 , 4,2 , −2,−4

Tell whether the relation is a function. 3,−2 , 6,1 , −3,5 , 4,1 5,1 , 5,3 , 7,1 , 8,4

Function Rules A function may be represented using a rule that relates one variable to another. Now the input variable and output variable are renamed.

independent variable dependent variable is the input variable (x) is the output variable (y) because its value depends on the value of the input variable

Ways to Look at a Function Verbal Rule The output is 3 more than the input. Equation y = x + 3 Table

How do you represent a function as a table? Create an x/y table. Choose values from the domain for the x. Plug each domain in to the function to find the value for the range (y) by performing the rule.

How do you represent a function as a rule? Use the form 𝑦=𝑎𝑥+𝑏 Find the value of a. Use change in output change in input Find the value of b but looking for y value when x is 0. If you don’t have 𝑥=0 then plug in an ordered pair and solve for b.

Write a rule for the function.

Write a rule for the function.

Write a rule for the function.

Write a rule for the function.

Flower Garden You have a flat of 12 plants that you are planting in a garden. Each time you put one plant in the garden, you have one less plant in the flat. Write a rule for the number of plants y you have left in the flat as a function of the number of plants x you have put in the garden so far.

Centerpieces A florist is making centerpieces for a charity event Centerpieces A florist is making centerpieces for a charity event. She is using 9 flowers in each centerpiece. Write a rule for the total number of flowers used as a function of the number of centerpieces created.

Kickboxing You join a kickboxing class at a local gym Kickboxing You join a kickboxing class at a local gym. The cost is $5 per class plus $25 for the initial membership fee. Write a rule for the total cost of the class in dollars as a function of the number of classes you attend. How much will it cost if you go to 8 classes?

Concert Tickets You are buying concert tickets that cost $15 each Concert Tickets You are buying concert tickets that cost $15 each. You can buy up to 6 tickets. Write the amount (in dollars) that you spend as a function of the number of tickets you buy. Identify the independent and dependent variables and the domain and range.

How do you represent functions as tables and rules?

Ticket Out the Door Write the function rule. Solve the problem on a piece of paper (put your name on it) and place it in the box on your way out… Write the function rule. x 1 2 3 4 5 y 6 7 8 9 10