Determining Functions: Vertical Line Test and X Values

The video tutorial explains the concept of functions, emphasizing the definition where each element of the domain is paired with exactly one element of the range. It covers the importance of domain and range, provides examples of functions and non-functions, and introduces the vertical line test as a graphical method to determine if a relation is a function. Additional examples and mapping diagrams are used to further clarify the concept.

What is the definition of a function?

• A relation where each element of the range is paired with multiple elements of the domain.

• A relation where each element of the range is paired with exactly one element of the domain.

• A relation where each element of the domain is paired with multiple elements of the range.

• A relation where each element of the domain is paired with exactly one element of the range.

Which of the following is true about the domain of a function?

• It can have multiple y values for a single x value.

• It is typically the x values.

• It is typically the y values.

• It can have repeating values.

Why is the set of ordered pairs (2, 4), (2, 3) not a function?

• Because the y values are different.

• Because the x values are different.

• Because the x value 2 repeats with different y values.

• Because the y values are the same.

What does the Vertical Line Test (VLT) help determine?

• If a graph is a function.

• If a graph is a line.

• If a graph is a circle.

• If a graph is a parabola.

In the Vertical Line Test, what indicates that a graph is not a function?

• The horizontal line hits the graph more than once at any point.

• The vertical line hits the graph exactly once at every point.

• The vertical line hits the graph more than once at any point.

• The horizontal line hits the graph exactly once at every point.

If an ordered pair relation has the same x value with different y values, is it a function?

• Yes, because the y values are different.

• No, because the x value repeats with different y values.

• No, because the y values are the same.

• Yes, because the x values are the same.

In a table, if an x value repeats with different y values, what does it indicate?

• It is a quadratic function.

• It is a linear function.

• It is not a function.

• It is a function.

Which of the following ordered pairs represents a function?

• (1, 2), (3, 4)

• (8, 9), (8, 10)

• (2, 3), (2, 4)

• (5, 6), (5, 7)

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

• An output has multiple inputs.

• Each output has exactly one input.

• An input has multiple outputs.

• Each input has exactly one output.

What is the key takeaway about functions from the video?

• Every x value can have multiple y values.

• Every y value can have only one x value.

• Every y value can have multiple x values.

• Every x value can have only one y value.