Functions, Domain and 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.

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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.

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How can you determine if a graph represents a function?

Back

You can determine if a graph represents a function by using the Vertical Line Test: if a vertical line intersects the graph at more than one point, it is not a function.

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What does interval notation represent?

Back

Interval notation is a way of writing subsets of the real number line, using parentheses and brackets to indicate whether endpoints are included.

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What does the notation [a, b) mean?

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The notation [a, b) means that 'a' is included in the interval (closed), while 'b' is not included (open).

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What does the notation (a, b) mean?

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The notation (a, b) means that both 'a' and 'b' are not included in the interval (open interval).

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What is the difference between domain in interval notation and inequality notation?

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Domain in interval notation uses brackets and parentheses to denote intervals, while inequality notation uses inequalities to describe the same set of values.

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

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The range of the function f(x) = x^2 is [0, ∞) because the output values (y-values) are always non-negative.

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What is the domain of the function f(x) = 1/x?

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The domain of the function f(x) = 1/x is all real numbers except x = 0, which can be written in interval notation as (-∞, 0) ∪ (0, ∞).