The question is: "using an example explain what the graph of a rational function looks like. contrast this with other functions we have studied." and this is what my teacher said: describe the graph of the basic rational function, f(x)=1/x. talk about its domain and range and compare the function to other ones, i. e. linear or quadratic or exponential. is greatly appreciated!

X^(-1) is asymptotic at x=0 and y=0, meaning the graph approaches these value but never seems cross them. As X goes to infinite, y goes to zero. As X goes to negative infinite, y goes to zero. As x goes to 0 from the left, y approaches negative infinite. As x approaches 0 from the right, y approaches positive infinite.
The graph almost looks quadratic, except you would have to replace the y axis with the line y=x