Understanding One-to-One Functions

The video tutorial explains how to determine if a graph represents a one-to-one function. It introduces the vertical line test to check if a graph is a function and the horizontal line test to verify if it's a one-to-one function. The tutorial provides examples of graphs, demonstrating how to apply these tests to identify functions and one-to-one functions. The key takeaway is that a graph must first be a function before it can be a one-to-one function.

What is the first step in determining if a graph is a one-to-one function?

• Perform the diagonal line test

• Check if the graph is linear

• Check if the graph is a function

• Perform the horizontal line test

What does the vertical line test help determine?

• If a graph is increasing

• If a graph is continuous

• If a graph is a function

• If a graph is a one-to-one function

How is the vertical line test performed?

• By drawing a horizontal line across the graph

• By checking if the graph is symmetric

• By passing a vertical line across the graph

• By calculating the slope of the graph

What is the purpose of the horizontal line test?

• To check if a function is one-to-one

• To determine if a graph is a function

• To find the slope of a graph

• To test if a graph is continuous

When does a graph pass the horizontal line test?

• When a vertical line intersects the graph at more than one point

• When a vertical line does not intersect the graph at more than one point

• When a horizontal line does not intersect the graph at more than one point

• When a horizontal line intersects the graph at more than one point

In the first example, why is the blue graph not a one-to-one function?

• It is not continuous

• It is not a function

• It fails the horizontal line test

• It fails the vertical line test

What conclusion can be drawn if a graph fails the vertical line test?

• The graph is not a function

• The graph is linear

• The graph is a one-to-one function

• The graph is continuous

In the third example, what makes the graph a one-to-one function?

• It is symmetric about the origin

• It passes only the horizontal line test

• It passes only the vertical line test

• It passes both the vertical and horizontal line tests

What is the result of the last graph analysis?

• It is a one-to-one function

• It is not a function

• It passes the horizontal line test

• It is a linear function

How many graphs in the examples were one-to-one functions?

• None

• One

• Two

• All of them