Transforming a function using a parent function

[SwimmingGoat]

Ok, I've been working on a long problem (if you want all the steps I've taken to get to this point, I'll give them to you, but they aren't relevant, and I've done them correctly), and now I'm slightly stuck.

Right now I have $$f(x)=\frac{x^2+2x}{2x+2}$$. The current problem asks me if the graph can be defined as a transformation of some base function whose graph we already know. I'm having a hard time coming up with a parent function/graph that will help me transform to this equation. Any ideas or thoughts? I thought of doing the reciprocal 1/x, but the degree in the numerator is larger than the denominator...

Thank you in advance!

 

[tiny-tim]

Hi SwimmingGoat!

Hint: long division?

 

[SwimmingGoat]

aha! Thank you! I knew I was missing an obvious place to start. This is what happens when I do math for three hours straight...