Understanding Functions and the Vertical Line Test

This video tutorial explains the concepts of relations and functions, focusing on how to identify functions using ordered pairs and the vertical line test. It covers the importance of non-repeating x-values in functions, demonstrates how to determine the domain and range, and illustrates the use of mapping diagrams. The video also provides examples of graphs to show how the vertical line test can be applied to determine if a relation is a function.

What is a key characteristic of a function?

• No repeating values in the codomain

• No repeating x-values

• No repeating values in the range

• No repeating y-values

Which of the following sets of ordered pairs represents a function?

• {(2, 3), (5, 4), (0, 3), (4, 1)}

• {(0, 0), (1, 1), (2, 2), (2, 3)}

• {(3, -1), (2, -2), (0, 2), (2, 1)}

• {(1, 2), (2, 3), (3, 4), (1, 5)}

What is the domain of the function represented by the ordered pairs {(2, 3), (5, 4), (0, 3), (4, 1)}?

• {3, 4, 3, 1}

• {2, 5, 0, 4}

• {0, 2, 4, 5}

• {1, 3, 4, 5}

How do you create a mapping diagram for a set of ordered pairs?

• List the x-values and y-values in separate columns

• Draw arrows from each x-value to its corresponding y-value

• Plot the points on a graph

• List the y-values and x-values in separate columns

Which of the following ordered pairs would not be included in the range of the function {(2, 3), (5, 4), (0, 3), (4, 1)}?

• 3

• 2

• 4

• 1

What does the vertical line test determine?

• If a graph is linear

• If a graph is a function

• If a graph has repeating y-values

• If a graph is continuous

What happens if a vertical line touches a graph at more than one point?

• The graph is a function

• The graph is not a function

• The graph is linear

• The graph is continuous

In the vertical line test, what does it mean if a vertical line touches the graph at exactly one point?

• The graph is not a function

• The graph is continuous

• The graph is a function

• The graph is linear

Which of the following graphs would pass the vertical line test?

• A graph where a vertical line touches it at two points

• A graph where a vertical line does not touch it at all

• A graph where a vertical line touches it at three points

• A graph where a vertical line touches it at one point

Why does a graph fail the vertical line test?

• Because it has repeating x-values

• Because it has repeating y-values

• Because a vertical line does not touch it at all

• Because a vertical line touches it more than once