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What is the range of a linear function?

Answer 1

Benjamin Achtenberg

The range of a linear function is all real numbers, #(-oo,oo).#

All of the #y# values on the number line are valid.

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Answer 2

Lincoln Anderson

The range of a linear function is the set of all possible output values (or y-values) that the function can produce given its domain. For a linear function in the form (f(x) = mx + b), where (m) is the slope and (b) is the y-intercept, the range is all real numbers if the slope is non-zero.

If the slope (m) is positive, the range is all real numbers greater than or equal to the y-intercept (b). If the slope (m) is negative, the range is all real numbers less than or equal to the y-intercept (b).

In other words, the range of a linear function is either all real numbers ((−∞ < y < +∞)) or a half-infinite interval depending on the direction of the slope.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.