Understanding One-to-One Functions

The video tutorial explains how to identify one-to-one functions from sets of ordered pairs. It begins by defining one-to-one functions and the importance of ensuring a relation is a function before checking if it is one-to-one. The tutorial then analyzes several relations (P, H, B, E, J) to determine if they are functions and subsequently if they are one-to-one. The video concludes by identifying which relations are one-to-one functions, providing a clear understanding of the concept.

What is a key characteristic of a one-to-one function?

• Each output has multiple inputs.

• Inputs and outputs are the same.

• Each output corresponds to exactly one input.

• Each input has multiple outputs.

What must be checked first before determining if a function is one-to-one?

• If the function is linear.

• If the relation is a function.

• If the function is quadratic.

• If the function is continuous.

How can you determine if a relation is a function?

• By checking if any y-values are repeated.

• By checking if the relation is symmetric.

• By checking if any x-values are repeated.

• By checking if the graph is a straight line.

Which relation was determined not to be a function due to repeated x-values?

• Relation H

• Relation B

• Relation P

• Relation J

What is the x-value that repeats in relation P?

• 13

• 9

• 3

• 5

Which function was found to have repeated y-values, making it not one-to-one?

• Function B

• Function J

• Function E

• Function H

What repeated y-value was found in function J?

• 0

• 1

• Negative 2

• Negative 1

Which functions were determined to be one-to-one?

• H, B, and E

• H, B, and J

• B, E, and J

• H, E, and J

What is the main criterion for a function to be one-to-one?

• Each x-value has multiple y-values.

• Each y-value corresponds to exactly one x-value.

• The function is a straight line.

• The function is quadratic.

Why is function J not considered one-to-one?

• It has repeated x-values.

• It is a quadratic function.

• It is not a function.

• It has repeated y-values.