Domain, Range and 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 complete set of possible values of the independent variable (input) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the complete set of possible values of the dependent variable (output) that results from using the function.

Front

How do you determine the domain of a function from its graph?

Back

The domain can be determined by identifying all the x-values that the graph covers.

Front

How do you determine the range of a function from its graph?

Back

The range can be determined by identifying all the y-values that the graph covers.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is associated with exactly one input, meaning no two different inputs produce the same output.

Front

What is a 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

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where for every input x, there is a unique output.

Front

What is an example of a non-function?

Back

An example of a non-function is the relation defined by the equation x^2 + y^2 = 1, as it can produce multiple y-values for a single x-value.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, typically in the form f(x) = mx + b.