Understanding Functions and One-to-One Functions

The video tutorial explains how to determine if relations in table form are functions and one-to-one functions. It begins by defining functions and one-to-one functions, emphasizing that a function has one output for each input, while a one-to-one function has unique outputs for each input. The tutorial then demonstrates mapping and testing three relations to identify if they are functions and one-to-one functions. The first relation is not a function, the second is a function but not one-to-one, and the third is both a function and one-to-one. The video concludes with a shortcut for identifying one-to-one functions.

What is a function in terms of input and output?

• A relation where inputs and outputs are the same

• A relation where each input has exactly one output

• A relation where each output has multiple inputs

• A relation where each input has multiple outputs

How can you determine if a function is one-to-one?

• Each output has a unique input

• Each output has multiple inputs

• Each input has a unique output

• Each input has multiple outputs

In the first table, why is the relation not a function?

• Because it has more y-values than x-values

• Because all y-values are unique

• Because all x-values are unique

• Because one x-value corresponds to two y-values

What is the key characteristic of the second table that makes it a function?

• Each x-value has multiple y-values

• Each y-value has exactly one x-value

• Each x-value has exactly one y-value

• Each y-value has multiple x-values

Why is the second table not a one-to-one function?

• Because one y-value corresponds to two x-values

• Because each y-value has a unique x-value

• Because each x-value has a unique y-value

• Because all y-values are unique

What makes the third table a one-to-one function?

• Each x-value has multiple y-values

• Each y-value has multiple x-values

• Each x-value and y-value are the same

• Each x-value has a unique y-value and vice versa

What is the shortcut for identifying a one-to-one function from a table?

• Repetition in y-values but not in x-values

• Repetition in both x-values and y-values

• Repetition in x-values but not in y-values

• No repetition in x-values or y-values