Justifying Relations as Functions

This video tutorial explains how to determine if a relation is a function, emphasizing that each x value must have one unique y value. It uses examples like birthdays and height to illustrate the concept. The tutorial also covers different ways to represent relations, such as ordered pairs, tables, and graphs, and introduces the vertical line test as a method to identify functions. Finally, it provides practice examples for viewers to apply their understanding.

What is the definition of a function in terms of x and y values?

• Each x value has one and only one corresponding y value.

• Each y value has one or more x values.

• Each x value has one or more y values.

• Each y value has one and only one corresponding x value.

Which of the following is an example of a function?

• A person can have multiple names.

• A person can have multiple birthdates.

• A person can have multiple heights.

• A person can have only one height.

In a set of ordered pairs, which value is considered the input?

• Both values are inputs.

• The second value in the pair.

• Neither value is an input.

• The first value in the pair.

What does it mean if an x value repeats with different y values in a mapping diagram?

• It depends on the number of repetitions.

• It depends on the y values.

• It is not a function.

• It is still a function.

In a table, what indicates that the relation is not a function?

• All y values are different.

• An x value is paired with multiple y values.

• All y values are the same.

• All x values are different.

What is the vertical line test used for?

• To determine if a graph represents a function.

• To determine if a mapping diagram represents a function.

• To determine if a table represents a function.

• To determine if ordered pairs represent a function.

What does it mean if a vertical line intersects a graph at more than one point?

• The graph represents a function.

• The graph does not represent a function.

• The graph represents multiple functions.

• The graph represents a single function.

In the given graph, why is it not a function?

• It has multiple x values.

• It has multiple y values.

• It fails the vertical line test.

• It passes the vertical line test.

In the given mapping diagram, why is it considered a function?

• Each y value has one and only one x value.

• Each y value has multiple x values.

• Each x value has one and only one y value.

• Each x value has multiple y values.

In the given table, why is it not a function?

• All x values are different.

• Each x value has one and only one y value.

• An x value is paired with multiple y values.

• All y values are the same.