1-4: Patterns and Functions

Essential Question:

1-4: Patterns and Functions A function is a relationship that assigns

exactly one output value for each input value. For each input value, there is only one corresponding output.

A function rule, such as C = p + 0.06p, is an equation that defines a functional relationship.

1-4: Patterns and Functions Example 1: Writing a Function Rule

The relationship between the number of loads of laundry and cost is given below. Use the table to write a function rule.

Determine variable names to use Let n = number of loads Let c = cost

Determine the difference between successive entries. $5.50 - $2.75 = $2.75 $8.25 - $5.50 = 2.75

$11.00 – $8.25 = 2.75 Work backwards to determine if there would have been

any cost with 0 loads. Nope

c = 2.75 • n

1-4: Patterns and Functions YOUR TURN: Writing a Function Rule

The relationship between the number of hours and the total miles driven is given below. Use the table to write a function rule.

m = 60 • h

1-4: Patterns and Functions Example 2: Writing a Function Rule (with starting

point) The relationship between the number of houses built and

number of toothpicks used.

Determine variable names to use Let h = number of houses Let t = number of toothpicks

Determine the difference between successive entries. 11 – 6 = 5 16 – 11 = 5 21 – 16 = 5

Work backwards to determine if there would have been any cost with 0 houses. 6 – 5 = 1

c = 5 • n + 1

1-4: Patterns and Functions YOUR TURN: Writing a Function Rule (with a

starting point) The relationship between an input (x) and output

(y) is given below. Determine the function for the data in the table.

y = 3x + 2

1-4: Patterns and Functions The relationship between the number of

houses built and number of toothpicks used.

In this example, the number of toothpicks tdepends on the number of houses h to bebuilt.

This makes t the dependent variable, and hthe independent variable.

In most real-world scenarios, the independent variable is the one you can control.

1-4: Patterns and Functions Example 3

The cost of a memory stick is shown in the table below. Determine the dependent and independent variables.

Because the cost DEPENDS on the amountof memory you wish to purchase, the costis the dependent variable

Because you control how much memory youwish to buy, memory is the INDEPENDENTvariable.

1-4: Patterns and Functions Your Turn

Determine the independent and dependent variable in the scenario below.

The cooking time for an unstuffed turkey is about 20 minutes per pound. Dependent variable: Independent variable:

The cooking timeThe number of pounds to cook

1-4: Patterns and Functions The possible values for input (or independent

variable) of a function are the domain of the function. The possible values of the output (dependent variable) are the range of the function.

Example 4: Reasonable domain and range Maria earns $7 an hour for babysitting after school and on

Saturday. She works no more than 16 hours a week. Identify the independent and dependent quantities

She controls the number of hours she works, so that is the independent variable.

The amount she earns is the dependent variable (her pay DEPENDS on the amount of hours she works)

Find a reasonable domain and range for this situation She works no more than 16 hours a week, so a reasonable

domain is anything from 0 to 16 hours. A reasonable range is anything from $0 to $112 (7 • 16)

1-4: Patterns and Functions Your Turn

Charlie downloads songs for $0.75 each. He has between $3.00 and $6.00 to spend on songs.

Identify the independent and dependent variables. Independent variable: The amount of money he decides

to spend Dependent variable: How many songs he downloads

Find a reasonable domain and range. Domain: Anything from $3 to $6 Range: Anything from 4 to 8 songs (3/0.75 and 6/0.75)

1-4: Patterns and Functions Assignment

Practice Worksheet 1-4 All problems

Tomorrow Quiz on Sections 1-1 through 1-3