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

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 inverse of a function?

Back

A function that reverses the effect of the original function, swapping the input and output.

Front

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

Back

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

Front

If f(x) = 2x + 3, what is f^{-1}(x)?

Back

f^{-1}(x) = (x - 3)/2.

Front

True or False: A function can be one-to-one if it has the same output for different inputs.

Back

False.

Front

What does it mean for a function to be not one-to-one?

Back

It means that there exists at least one pair of different inputs that produce the same output.

Front

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

Back

f(x) = x^3 is a one-to-one function because it passes the horizontal line test.

Front

What is the domain of the function f(x) = x^2?

Back

The domain is all real numbers, but it is not a one-to-one function.

Front

What is the range of the function f(x) = x^2?

Back

The range is all non-negative real numbers.