How to graph $\frac{(x+3)}{(x+1)}$?

Question

I'm not looking for plotting values. I mean something which can be done without it.

For example, for the function $f(x) = mx + b$, we can use the slope $m$ and the y-intercept $b$ to easily graph the function, but the function given above seems impossible to graph like that. Any hints?

Answer 1

$$y=\frac{x+3}{x+1}=\frac{(x+1)+2}{x+1}=1+\frac2{x+1}$$

$$y=\frac2x \rightarrow y=\frac2{x+1}\rightarrow y= 1+\frac2{x+1}$$