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How do you find the domain and range of #y = log_2(x - 3)#?

Answer 1

Benjamin Achtenberg

The argument of a log-function must be positive.

This means #x-3>0->x>3#

If #x# gets closer to #3#, the log will get more and more negative

Or, in the "language"" #lim_(x->3) log_2 (x-3)= -oo#

The other way, #x# getting larger, will get the function larger: #lim_(x-> oo) log_2 (x-3) = oo#

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Answer 2

Sophie Adams

The domain of the function ( y = \log_2(x - 3) ) is ( x > 3 ), and the range is ( y \in \mathbb{R} ).

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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.