Functions

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 vertical line test?

Back

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

Front

What is a domain in 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 a range in a function?

Back

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

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, but each input must have only one output.

Front

What is an example of a function?

Back

An example of a function is f(x) = x + 2, where for each value of x, there is a unique value of f(x).

Front

What is a relation?

Back

A relation is a set of ordered pairs, which may or may not be a function.

Front

Is the set {(1,2), (2,4), (1,5)} a function?

Back

No, it is not a function because the input '1' is associated with two different outputs (2 and 5).

Front

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

Back

A function is one-to-one if it never assigns the same value to two different domain elements.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form f(x) = mx + b, where m and b are constants.