Question

I have a question-
The range of y = 1/(x-5) is All real Numbers

True or False

I think it is false because it should be all real numbers except y shouldn't equal 0. Is that correct or don't I understand it-Please explain if I'm wrong.
Thanks

Answer 1

you are correct,
If you graph it, the graph will approach the x-axis , but will never reach it.
For large positive values of x, the graph will be slightly above the x-axis,
for large negative values of x, the graph will be slightly below the x-axis

if you solve
0 = 1/(x-5) and cross-multiply , you get
0 = 1 which of course is a contradiction. Thus our equaiton cannot have a solution, that is, y can never be zero.