Understanding Functions: One-to-One and Onto

The video tutorial explains how to classify functions as one-to-one, onto, both, or neither. It introduces the vertical line test to verify if a graph represents a function and the horizontal line test to determine if a function is one-to-one. The tutorial further explains that a function is onto if it covers all y-values. Examples are provided to illustrate these concepts, and the classifications for four graphs are discussed.

What is the purpose of the vertical line test?

• To find the domain of a function

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

• To verify if a graph represents a function

• To check if a function is onto

Which test is used to determine if a function is one-to-one?

• Slope test

• Vertical line test

• Diagonal line test

• Horizontal line test

What does it mean if a horizontal line intersects a graph at more than one point?

• The function is neither one-to-one nor onto

• The function is onto

• The function is not one-to-one

• The function is both one-to-one and onto

In a one-to-one function, what is true about the y-values?

• Each y-value has at most one corresponding x-value

• Y-values are always positive

• Y-values can be repeated

• Y-values are always negative

What is an injective function?

• A function where different inputs have the same output

• A function where different inputs have different outputs

• A function that is not a function

• A function that is both one-to-one and onto

How can you determine if a function is onto?

• By using the vertical line test

• By checking if the graph covers all y-values

• By using the diagonal line test

• By checking if the graph covers all x-values

What is true about a function that is onto?

• Every output in the range is the output of some input

• The function is only one-to-one

• Every input has multiple outputs

• The function is not a function

Which graph characteristic indicates a function is not onto?

• The graph is a parabola

• The graph does not reach all y-values

• The graph has a hole

• The graph is a straight line

For the first graph, what classification is correct?

• One-to-one

• Both one-to-one and onto

• Onto

• Neither

What classification applies to the third and fourth graphs?

• Both one-to-one and onto

• Neither

• Only onto

• Only one-to-one