Domain, Range, and Functions

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input from its domain.

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 is associated with exactly one output. This can be tested using the vertical line test.

Front

What is the vertical line test?

Back

The vertical line test states that if a vertical line intersects a graph at more than one point, then the graph does not represent a function.

Front

What does it mean if a mapping diagram does not represent a function?

Back

If a mapping diagram does not represent a function, it means that at least one input is associated with multiple outputs.

Front

Can a function have a domain that includes all real numbers?

Back

Yes, a function can have a domain of all real numbers, which is denoted as (-∞, ∞).

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 y^2 = x, where each positive x value corresponds to two y values (positive and negative).

Front

What is the significance of the range in a function?

Back

The range indicates the possible outputs of a function, which helps in understanding the behavior and limitations of the function.