graphing question - y=((x-4)^2)/(x-2)?

Question

I tried to graph that, but it came out with a line. I think it's because my graphing calculator expanded the top to (x+2)(x-2), and then the (x-2)'s cancel out.

So, how would you graph this question? I need to find the domain, range, intercepts, and asymptotes. All i know is that the asymptote is 2.

Answer 1

Good job. That's exactly what it is. With the exception of when x = 2. Then you have zero in the denominator which you have to avoid. You do that by eliminating 2 from the domain. The graph is the line, y = x + 2, with a "hole" in it at (2, 4). y-intercept at (0, 2), x-intercept at (-2, 0), No asymptotes.
Domain, all real numbers except 2.
Range, all real numbers except 4.