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 domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

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

What does it mean for a relation to be a function?

Back

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

Front

How do you determine if a mapping is a function?

Back

A mapping is a function if no two ordered pairs have the same first element (x-value) with different second elements (y-values).

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

Evaluate f(0) for the function f(x) = -3x + 3.

Back

f(0) = 3.

Front

Solve for x in the equation f(-11) = 5x + 1.

Back

x = -11.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 1, where for each x, there is a unique y.

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.