In this Grade 8 Illustrative Mathematics lesson from Chapter 5, students explore input-output rules and learn the definition of a function as a rule that assigns exactly one output to each allowable input. Through activities like completing tables and identifying "black box" rules, students practice applying operations such as addition, multiplication, and division to determine outputs from given inputs. The lesson also addresses why certain inputs are not allowable, using division by zero as a key example of an undefined output.
Section 1
Using Input-Output Tables
An input-output table organizes pairs of numbers that are related by a rule. The 'input' is the number you start with, and the 'output' is the result after applying the rule. We often use variables like for the input and for the output.
Section 2
Completing an Input-Output Table
To find the output for a given input , substitute the value of into the function's rule and evaluate the expression.
Section 3
Definition of a Function
A function is a relationship between two variables for which a unique value of the output variable can be determined from a value of the input variable.
The input variable is also called the independent variable, and the output variable is the dependent variable.
This unique value property is what distinguishes functions from other variable relationships; exactly one output value corresponds to each input value.
Think of a function like a coffee machine. You press one button (the input), and you get exactly one type of coffee (the unique output). You can't press the espresso button and sometimes get a latte. Each input has only one result.
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Section 1
Using Input-Output Tables
An input-output table organizes pairs of numbers that are related by a rule. The 'input' is the number you start with, and the 'output' is the result after applying the rule. We often use variables like for the input and for the output.
Section 2
Completing an Input-Output Table
To find the output for a given input , substitute the value of into the function's rule and evaluate the expression.
Section 3
Definition of a Function
A function is a relationship between two variables for which a unique value of the output variable can be determined from a value of the input variable.
The input variable is also called the independent variable, and the output variable is the dependent variable.
This unique value property is what distinguishes functions from other variable relationships; exactly one output value corresponds to each input value.
Think of a function like a coffee machine. You press one button (the input), and you get exactly one type of coffee (the unique output). You can't press the espresso button and sometimes get a latte. Each input has only one result.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter