2.1 Identifying Functions and Domain/Range

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 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 the domain from a graph?

Back

To determine the domain from a graph, identify the x-values that the graph covers.

Front

How do you determine the range from a graph?

Back

To determine the range from a graph, identify the y-values that the graph covers.

Front

What does it mean for a table to represent y as a function of x?

Back

A table represents y as a function of x if each x-value corresponds to exactly one y-value.

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What is an example of a function?

Back

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

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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 input 1 corresponds to two different outputs.

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 notation for domain is often expressed as D(f) or simply as the set of x-values.