One-to-One functions

Front

What is a one-to-one function?

Back

A function where each output is associated with exactly one input, meaning no two different inputs produce 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, it is not a one-to-one function.

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 bijection.

Front

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

Back

It means that for at least one input, there is more than one output, violating the definition of a function.

Front

Give an example of a one-to-one function.

Back

f(x) = 2x + 3 is one-to-one because each input x produces a unique output.

Front

Give 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

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

Back

One-to-one functions are important for establishing invertibility; if a function is one-to-one, it has an inverse.

Front

How can you determine if a function is one-to-one from its graph?

Back

By applying the horizontal line test; if any horizontal line intersects the graph more than once, it is not one-to-one.

Front

What is the definition of a function?

Back

A relation where each input is associated with exactly one output.