One to One Functions

Front

What is a one-to-one function?

Back

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

Front

What is the vertical line test?

Back

A method to determine if a graph represents a function; if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the horizontal line test?

Back

A method to determine if a function is one-to-one; if a horizontal line intersects the graph at more than one point, the function is not one-to-one.

Front

Can a function be both one-to-one and onto?

Back

Yes, a function can be both one-to-one (injective) and onto (surjective), making it a bijective function.

Front

What does it mean if a function is not one-to-one?

Back

It means that there are at least two different inputs that produce the same output.

Front

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

Back

f(x) = 2x is a one-to-one function because each input x produces a unique output.

Front

What is an example of a function that is not one-to-one?

Back

f(x) = x^2 is not one-to-one because both -2 and 2 produce the same output (4).

Front

How can you determine if a function is one-to-one using its equation?

Back

You can check if the equation passes the horizontal line test by solving for y and checking if each y-value corresponds to only one x-value.

Front

What is the significance of one-to-one functions in mathematics?

Back

One-to-one functions are important because they allow for the existence of an inverse function.

Front

What is the relationship between one-to-one functions and inverses?

Back

Only one-to-one functions have inverses that are also functions.