Flashcard review: Identifying and Evaluating Functions

Front

What is the definition of a function?

Back

A function is a relation in which each input (x-value) is associated with exactly one output (y-value).

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 do you determine if a relation is a function?

Back

A relation is a function if every x-value has only one corresponding y-value.

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each x-value has a unique y-value.

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)}, where the x-value 1 has two different y-values.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function; if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the notation for domain?

Back

The domain is often expressed in interval notation, such as (-∞, +∞) or [a, b].

Front

What is the notation for range?

Back

The range is also expressed in interval notation, such as (-∞, +∞) or [c, d].