domain and range of a linear function

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The domain and range are concepts used in mathematics, particularly in the study of functions, to describe the sets of input and output values, respectively.

The domain and range of a linear function can be determined based on its equation or graph.

  1. Domain of a Linear Function:
    • The domain of a linear function is the set of all possible input values (x-values) for which the function is defined.
    • Since a linear function continues indefinitely in both directions along the x-axis, its domain is all real numbers unless there are specific restrictions mentioned in the context of the problem.
  2. Range of a Linear Function:
    • The range of a linear function is the set of all possible output values (y-values) that the function can produce.
    • For a linear function in the form y = mx + b, where m represents the slope and b represents the y-intercept, the range is also all real numbers, as the function extends infinitely along the y-axis.

In summary, the domain of a linear function is all real numbers, and the range of a linear function is also all real numbers. This is true for most linear functions unless there are specific restrictions or conditions mentioned that limit the domain or range.

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