Understanding Functions from Tables

The video tutorial explains how to determine if tables represent functions by analyzing input-output relationships. A function is defined as a relation where each input has exactly one output. The tutorial examines three tables, using mapping to visualize relationships. The first and third tables are not functions because they have inputs with multiple outputs. The second table is a function as each input has a single output, even if outputs repeat.

What is a function in terms of input and output?

• A relation where each input has multiple outputs

• A relation where inputs are equal to outputs

• A relation where each input has exactly one output

• A relation where outputs are greater than inputs

Why does the first table not represent a function?

• It has more outputs than inputs

• It has repeated inputs with different outputs

• It has no outputs

• It has repeated outputs with different inputs

What is the purpose of mapping in understanding functions?

• To list all possible outputs

• To show the relationship between inputs and outputs

• To calculate the sum of inputs

• To find the average of outputs

In the second table, why is it considered a function?

• Each input has exactly one output

• Each output is greater than the input

• Each input has multiple outputs

• Each output has multiple inputs

What is unusual about the mapping in the second table?

• All outputs map to the same input

• All inputs map to the same output

• Multiple inputs map to the same output

• No inputs map to any output

Why does the third table not represent a function?

• It has repeated outputs with different inputs

• It has more outputs than inputs

• It has repeated inputs with different outputs

• It has no inputs

In the third table, which input is repeated with different outputs?

• Two

• Four

• Negative one

• Zero

What is the key characteristic of a function in a table?

• Each input has exactly one output

• Each output has multiple inputs

• Each input has multiple outputs

• Each output is less than the input

How can mapping help in identifying functions?

• By listing all inputs

• By showing all possible outputs

• By illustrating the input-output relationship

• By calculating the difference between inputs and outputs

What does it mean if an input has two arrows pointing to different outputs in mapping?

• The table is a function

• The table is not a function

• The inputs are incorrect

• The outputs are incorrect