Exploring Functions and Relations

The video tutorial covers the concept of functions and relations, emphasizing the definition of a function as a rule that assigns each input exactly one output. It includes exercises to identify and verify functions using graphs, tables, and mapping diagrams. The tutorial also explores non-numerical functions and the vertical line test as a method to determine if a graph represents a function.

What is the definition of a function?

• A rule that converts an input into no outputs

• A rule that converts an input into exactly two outputs

• A rule that converts an input into at most one output

• A rule that converts an input into multiple outputs

Which of the following statements is true about functions?

• Every x value can have multiple y values

• Every y value can have multiple x values

• Every x value has only one y value

• Every y value has only one x value

Why is the relation with the points (2, 3) and (2, -1) not a function?

• Because the y value 3 has two different x values

• Because it has more than one y value

• Because the x value 2 has two different y values

• Because it has more than one x value

How are ordered pairs listed in set notation?

• Using angle brackets

• Using square brackets

• Using round brackets

• Using curly brackets

What does a mapping diagram show?

• The relationship between x values and z values

• The relationship between x values and y values

• The relationship between y values and z values

• The relationship between y values and w values

In a mapping diagram, what indicates that a relation is not a function?

• A y value is mapped to a single x value

• An x value is mapped to a single y value

• A y value is mapped to multiple x values

• An x value is mapped to multiple y values

Why is the relation in Exercise 2 considered a function?

• Because each x value has multiple y values

• Because each y value has multiple x values

• Because each x value has only one y value

• Because each y value has only one x value

What is the significance of the vertical line test?

• It determines if a graph has multiple x values

• It determines if a graph has multiple y values

• It determines if a graph represents a function

• It determines if a graph represents a relation

What happens 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 a relation

• The graph does not represent a relation

Which ordered pair would make the relation no longer a function if added to the table?

• (1, -4)

• (3, 2)

• (-4, 1)

• (2, 3)