Determining Functions Through Various Representations

This video tutorial explains how to determine if a relation is a function. It begins by defining relations and functions, emphasizing that functions are a special type of relation where each domain value pairs with exactly one range value. The video uses mapping diagrams and examples to illustrate this concept. It also covers different representations of functions, such as ordered pairs, tables, graphs, and equations. The tutorial explains the vertical line test as a method to identify functions and provides examples of non-functions. Finally, it offers tips on explaining whether a relation is a function.

What are the x-coordinates in a set of ordered pairs also known as?

• Output

• Input

• Range

• Function

Which of the following statements is true about functions?

• A function can have multiple outputs for a single input.

• A function is a special type of relation where each input has exactly one output.

• A function can have repeating domain values.

• A function is not a subset of relations.

In a mapping diagram, what does it mean if a domain value is paired with more than one range value?

• It is a linear equation.

• It is not a function.

• It is a vertical line.

• It is a function.

Which representation of a function shows that every point on the line has a different domain value?

• Table

• Ordered pairs

• Graph

• Mapping diagram

Which of the following is an example of a function?

• A mapping diagram where one x value maps to multiple y values.

• A vertical line graph.

• A table where the x values are different.

• A set of ordered pairs where the x values repeat.

What is the vertical line test used for?

• To identify the domain of a function.

• To calculate the slope of a line.

• To find the range of a function.

• To determine if a relation is a function.

If a vertical line touches a graph in more than one place, what can be concluded?

• The graph does not represent a function.

• The graph is a linear equation.

• The graph represents a function.

• The graph is a horizontal line.

What is the equation of a vertical line graph?

• y = mx + b

• x = a constant value

• y = a constant value

• x = y

Which of the following is NOT a valid response when explaining why something is a function?

• The x values do not repeat.

• The domain values do not repeat.

• It passes the vertical line test.

• The y values do not repeat.

What must you clarify when stating that something is a function because the values do not repeat?

• That the output values do not repeat.

• That the domain or x values do not repeat.

• That the y values do not repeat.

• That the range values do not repeat.