Understanding One-to-One Functions

The video tutorial explains how to determine if a graph represents a one-to-one function. It covers the vertical line test to check if a graph is a function and the horizontal line test to verify if it's one-to-one. Several examples are provided, including graphs that are functions but not one-to-one, graphs that are not functions, and a piecewise-defined function. The tutorial concludes with an example of a graph that is a one-to-one function.

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

• Check for symmetry

• Use the horizontal line test

• Use the vertical line test

• Calculate the slope

What does it mean if a graph passes the vertical line test?

• It is a one-to-one function

• It is a linear function

• It is a function

• It is not a function

In Example 1, why does the graph fail the horizontal line test?

• It does not intersect the graph

• It intersects the graph at exactly one point

• It intersects the graph at more than one point

• It is a vertical line

What conclusion is drawn from Example 1 regarding the graph?

• It is neither a function nor one-to-one

• It is a one-to-one function

• It is not a function

• It is a function but not one-to-one

In Example 2, what is the result of the vertical line test?

• The graph is not a function

• The graph is a function

• The graph is linear

• The graph is one-to-one

Why is the graph in Example 2 not a one-to-one function?

• It fails the vertical line test

• It is a piecewise function

• It passes the vertical line test

• It passes the horizontal line test

In Example 3, what characteristic of the piecewise-defined function is highlighted?

• It has open and closed points

• It is a linear function

• It fails the vertical line test

• It has no open points

What is the outcome of the horizontal line test for the piecewise-defined function in Example 3?

• It is inconclusive

• It fails the test

• It is not applicable

• It passes the test

In Example 4, what is the result of the vertical line test?

• The graph is not a function

• The graph is undefined

• The graph is not one-to-one

• The graph is a function

What makes the graph in Example 4 a one-to-one function?

• It is a quadratic function

• It passes both the vertical and horizontal line tests

• It fails the horizontal line test

• It is a piecewise function