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 definition of a function?

Back

A relation where each input (x) has exactly one output (y).

Front

How can you determine if a relation is a function?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What does the horizontal line test determine?

Back

It determines if a function is one-to-one; if any horizontal line intersects the graph more than once, it is not a one-to-one function.

Front

What is the domain of a function?

Back

The set of all possible input values (x) for the function.

Front

What is the range of a function?

Back

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

Front

If a function has a domain of {2, 3, 5}, what is the range if it is one-to-one?

Back

The range must also consist of three unique values, one for each input.

Front

True or False: For a function to be one-to-one, every y must correspond to exactly one x.

Back

True.

Front

What is the inverse of a function?

Back

A function that reverses the mapping of the original function, swapping the roles of inputs and outputs.

Front

How do you find the inverse of a function?

Back

Replace f(x) with y, swap x and y, and then solve for y.