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What is the domain and range for #y=4absx-1#?

Answer 1

Domain: #(-oo,oo)#
Range: #[-1,oo)#

The domain is all real numbers because you can multiply 4 by any number from -infinity to infinity, although the only value used will be the absolute value. For example, if x= - 7 then y=27 because #4*|-7|-1=4*7-1#.

Because x is absolute value, the lowest number you can have is zero. #4*0-1=-1# thus making -1 the lowest value you can have for y.

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Answer 2

Eva Abramson

The domain of the function y = 4|abs(x)| - 1 is all real numbers (-∞, ∞). The range of the function y = 4|abs(x)| - 1 is [−1, ∞).

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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.