Functions, Domain and Range

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) that the function can accept.

Front

What is the range of a function?

Back

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

Front

How do you determine if a relation is a function?

Back

A relation is a function if every input (x-value) is associated with exactly one output (y-value).

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where for each x-value, there is one corresponding y-value.

Front

What is an example of a relation that is not a function?

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, because the input 1 is associated with two different outputs.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if 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 to determine if a curve is a function. If a vertical line intersects the curve at more than one point, it is not a function.

Front

Given the function y = x^2, what is the range?

Back

The range of the function y = x^2 is all non-negative real numbers, or [0, ∞).

Front

What is the domain of the function f(x) = 1/x?

Back

The domain of the function f(x) = 1/x is all real numbers except x = 0.