Functions: Different values of y for same value of x

In summary, functions are mathematical relationships between two or more variables, represented as y = f(x), where y is the dependent variable and x is the independent variable. When different values of y are produced for the same value of x, it means the function is a many-to-one relationship. A function can also have the same value of y for different values of x, known as a one-to-many or non-injective function. The difference between a one-to-one function and a many-to-one function is that in a one-to-one function, each value of x has a unique value of y, while in a many-to-one function, multiple values of y can result from the same value of x. The easiest way to determine if a function
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ScienceNerd36
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Is it possible to create a function that has two values of y for every one value of x, or is this an unbreakable rule of functions?
 
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ScienceNerd36 said:
Is it possible to create a function that has two values of y for every one value of x, or is this an unbreakable rule of functions?

Multivalued functions exist, but they're not functions.
 
  • #3
Thanks :)
 

FAQ: Functions: Different values of y for same value of x

What are functions?

Functions are mathematical relationships between two or more variables, where one variable (known as the independent variable) affects the value of another variable (known as the dependent variable). Functions are commonly represented as y = f(x), where y is the dependent variable and x is the independent variable.

What does it mean when different values of y are produced for the same value of x?

This means that the function is not a one-to-one relationship, and the same value of the independent variable (x) can result in multiple values of the dependent variable (y). This is known as a many-to-one function.

Can a function have the same value of y for different values of x?

Yes, this is known as a one-to-many function, where different values of the independent variable (x) can produce the same value of the dependent variable (y). This is also known as a non-injective function.

What is the difference between a one-to-one function and a many-to-one function?

A one-to-one function is a relationship where each value of the independent variable (x) has a unique value of the dependent variable (y). This means that no two different values of x can produce the same value of y. In contrast, a many-to-one function can have multiple values of y for the same value of x.

How can I determine if a function is one-to-one or many-to-one?

The easiest way to determine if a function is one-to-one or many-to-one is by graphing it. If the graph passes the horizontal line test (no horizontal line intersects the graph more than once), then the function is one-to-one. If the graph fails the horizontal line test, then it is many-to-one.

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