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Question 713997: Find the domain and range of the function:
g(x) = 9/(x-1)
I need help determining the range. I understand that domain contains all real numbers but 1.
Answer by josgarithmetic(39630)   (Show Source):
You can put this solution on YOUR website! You want to find the set of values that g(x) can be. You are not interested in what is g(x) at x=1, since g(x) has no meaning there. The meaningful ideas come from what happens NEAR x=1 to the left and to the right of x=1; and what happens as x goes unbounded toward negative and to positive infinities.
Near x=1 on the left, g is negative and decreases without bound as x moves toward 1. As x goes further and further to the left, g begins to approach 0, but still g<0.
Near x=1 on the right, g is now positive and increases upward without bound as x approaches 1, but as x goes to the right further and further, g moves toward 0 but g>0.
Put the two together and g takes on all real numbers from negative infinity to positive infinity.
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