One-to-One functions

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is produced by exactly one input, meaning no two different inputs map to the same output.

Front

How can you determine if a function is one-to-one using the horizontal line test?

Back

If any horizontal line intersects the graph of the function at most once, then the function is one-to-one.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

Front

What does it mean if a relation is not a function?

Back

A relation is not a function if at least one input is associated with more than one output.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How do you find the inverse of a function?

Back

To find the inverse of a function, swap the input and output values and solve for the new output.

Front

What is the relationship between the domain of a function and the range of its inverse?

Back

The domain of a function becomes the range of its inverse, and the range of the function becomes the domain of its inverse.

Front

Can a function have more than one inverse?

Back

No, a function can have at most one inverse if it is a one-to-one function.

Front

What is an example of a one-to-one function?

Back

An example of a one-to-one function is f(x) = 2x + 3, where each x-value produces a unique y-value.