One to one function

Front

What is a one-to-one function?

Back

A one-to-one function is 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

The vertical line test is a method used to determine if a relation is a function. If a vertical line intersects the graph at more than one point, the relation is not a function.

Front

What is the horizontal line test?

Back

The horizontal line test is used 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

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 multiple outputs.

Front

Can a one-to-one function also be a function?

Back

Yes, all one-to-one functions are functions, but not all functions are one-to-one.

Front

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

Back

An example of a one-to-one function is f(x) = 2x, where each input x produces a unique output.

Front

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

Back

An example of a function that is not one-to-one is f(x) = x^2, where both -2 and 2 produce the same output (4).

Front

What is the definition of a function?

Back

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

Front

What is the difference between a function and a relation?

Back

A relation is a set of ordered pairs, while a function is a specific type of relation where each input has a unique output.

Front

What is the significance of the horizontal line test in identifying one-to-one functions?

Back

The horizontal line test helps to identify one-to-one functions by checking if any horizontal line intersects the graph more than once.