Functions(Domain and Range)

Front

What is a function?

Back

A function is a relation between a set of inputs (domain) and a set of possible outputs (range) where each input is related to exactly one output.

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What is the domain of a function?

Back

The domain of a function is the complete set of possible values of the independent variable (usually x) that can be used in the function.

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What is the range of a function?

Back

The range of a function is the complete set of possible values of the dependent variable (usually y) that can result from using the function.

Front

How can you determine if a mapping diagram represents a function?

Back

A mapping diagram represents a function if each input (x-value) is connected to exactly one output (y-value). If any input is connected to more than one output, it is not a function.

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What does it mean if a table does not represent a function?

Back

If a table does not represent a function, it means that at least one input (x-value) is associated with more than one output (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 for each x-value, there is a unique y-value.

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What is an example of a non-function?

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An example of a non-function is the relation {(1, 2), (1, 3)}, where the input 1 is associated with two different outputs.

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What is the vertical line test?

Back

The vertical line test is a method used to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the graph does not represent a function.

Front

If a function has a domain of x ≥ -3, what does this mean?

Back

This means that the function accepts all values of x that are greater than or equal to -3.

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What are the possible values of the range if all range values are positive?

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If all range values are positive, then the range consists of all positive numbers greater than zero.