Can anyone explain what (1-x)^2 - y^2 > 1 should look like when graphed?
Notice that TheEmptySet is using the fact that "f(x)= g(x)" forms the boundary between "f(x)< g(x)" and "f(x)> g(x)".
To graph , first graph which is the hyperbola TheEmptySet shows. Then notice that x= 0,y= 0 ((0,0), the point between the two branchs of the hyperbola) does NOT satisfy the inequality you want. Therefore, the graph you want is the region "inside" each branch of the hyperbola that is shaded in TheEmptySet's graph.