Domain, Range, and Functions

Front

What is the definition of 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

How can you determine if a relation is a function?

Back

A relation is a function if every input value corresponds to exactly one output value. This can be checked using the vertical line test on a graph.

Front

What does it mean if a function is not defined for certain x-values?

Back

If a function is not defined for certain x-values, those values are excluded from the domain of the function.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function by checking if any vertical line intersects the curve at more than one point.

Front

What is an example of a function?

Back

An example of a function is f(x) = x^2, where each input x has a unique output x^2.

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 the relation defined by the equation x^2 + y^2 = 1, which gives two outputs for some inputs.

Front

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

Back

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

Front

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

Back

The range of f(x) = x^2 is all real numbers y such that y ≥ 0.