FLASHCARD 3.1a-c Domain, Range, Functions

Front

What is the definition of a function?

Back

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

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

Front

What does it mean if a relation is not a function?

Back

It means that at least one input is associated with multiple outputs.

Front

What is the notation used to represent the domain of a function?

Back

The domain is often represented using interval notation, set notation, or inequalities.

Front

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

Back

The range is [0, ∞) since the output values are all non-negative.

Front

What is an example of a function with a restricted domain?

Back

f(x) = √x has a domain of [0, ∞) because square roots of negative numbers are not defined in the real number system.

Front

What is the significance of the endpoints in a domain expressed in interval notation?

Back

Endpoints indicate whether the values are included (closed interval) or not included (open interval) in the domain.

Front

How do you find the domain of a rational function?

Back

The domain of a rational function is all real numbers except where the denominator equals zero.