Domain and Range in Context

Front

What is the definition of 'Domain' in mathematics?

Back

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

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What is the definition of 'Range' in mathematics?

Back

The range of a function is the complete set of possible values of the dependent variable (output) that results from using the function.

Front

What does it mean for a function to have 'all real numbers' as its domain?

Back

It means that the function can accept any real number as an input without restrictions.

Front

What does it mean for a function to have 'whole numbers' as its range?

Back

It means that the output of the function can only be whole numbers (0, 1, 2, 3, ...).

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Back

This implies that the function is defined for all values of n between 12 and 52, inclusive.

Front

What is an example of a function with a range of 'all positive integers'?

Back

An example is the function f(n) = n, where n is a positive integer.

Front

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

Back

The domain can be determined by identifying the x-values for which the graph exists (where the function is defined).

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Back

It indicates that the function is defined for all x-values that are greater than or equal to 0.

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What does it mean if a function's range is 'all real numbers greater than or equal to 3'?

Back

It means that the output of the function can take any real number value starting from 3 and extending to infinity.

Front

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

Back

The domain is all real numbers except x = 0, since division by zero is undefined.