Question 713997
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.