Algebra question

Question

The range of the function f : f(x) = x² - 1 ÷ x - 1 is ....

Can somone please help me to understand how to get the range of a function, Thank you very much

Answer 1

Main thing in this problem is exclude an x value that makes a denominator = 0. That means x cannot = 1

the domain is all real numbers except 1

the range is all possible value of y or f(x), which is all real numbers except 0, as x=1 would make f(x) undetermined

f(1) = (1^2-1)/(1-1) = 0/0

but x-1 = 1-1 = 0, the graph of the function is a straight line, but with a "hole" in it at the point (1,0).

range is all possible y values, which is all real numbers except y=0