Domain, Range, & Functions

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.

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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 of a function from a graph?

Back

To determine the domain from a graph, identify the x-values that the graph covers. Look for any restrictions such as vertical asymptotes or holes.

Front

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

Back

To determine the range from a graph, identify the y-values that the graph covers. Look for any restrictions such as horizontal asymptotes or gaps.

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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 a function?

Back

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

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What is an example of a function?

Back

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

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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 domain of the function f(x) = 1/(x-2)?

Back

The domain of f(x) = 1/(x-2) is all real numbers except x = 2, since the function is undefined at that point.

Front

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

Back

The range of f(x) = x^2 is all real numbers y such that y ≥ 0, since the output is always non-negative.