Question: this is a question regarding rational functions. the function f(x)=x^2/x is a rational function. Based on the rules of rational functions this function should have a vertical asymptote at 0 and a slant asymptote x and a hole at x=0. But the graph of f(x)=x^2/x is just the line f(x)=x. This is not a homework question, I am just very confused about why this is. Thanks for reading
First, based on the original form of f(x) note that x=0 is not in the domain. Simplify if possible before trying to figure out what features it has. It simplifies to f(x)=x, where x is not 0. Since the x in the denominator disappeared and there is nothing else to make it undefined, there is no vertical asymptote, just a hole at x=0 because of the domain. There is no slant asymptote, the graph is just a line y=x with the hole.