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How do you find the domain and range of #y = - sqrt(1 - x)#?

Answer 1

Hazel Anglin

See below.

For real numbers the radicand must be positive or 0. #(1 - x) >= 0# if #x## <= #1.

So domain is #{x in RR | x <= 1}#

Range is #{y in RR | y<= 0 }#

or using interval notation:

#(-oo , 1 ]#

#(-oo , 0 ]#

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Answer 2

Hazel Anglin

The domain of the function is all real numbers x such that ( 1 - x \geq 0 ), which gives ( x \leq 1 ). So, the domain is ( (-\infty, 1] ). The range is all real numbers y such that ( y \leq 0 ), so the range is ( (-\infty, 0] ).

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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.