Domain and Range

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What is the definition of 'Domain' in mathematics?

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The domain of a function is the complete set of possible values of the independent variable (usually x) for which the function is defined.

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What is the definition of 'Range' in mathematics?

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

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How do you determine the domain of a function from its graph?

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The domain can be determined by identifying all the x-values for which the graph has points. It includes all x-values that do not lead to undefined expressions.

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

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The range can be determined by identifying all the y-values that the graph reaches. It includes all y-values that correspond to the x-values in the domain.

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It means that x can take any value from a to b, including the endpoints a and b.

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It means that y can take any value between a and b, but not including the endpoints a and b.

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This implies that the function is defined for all x-values from 1 to 5, including both 1 and 5.

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This implies that the function can take any value less than or equal to 3.

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The domain is all real numbers except x = 0, since the function is undefined at x = 0.

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The range is all real numbers greater than or equal to 0, since the output of the function is always non-negative.