How do you graph a rational function?

Answer 1

It's definitely a process.

1. Find the asymptotes. The vertical asymptote is the number that makes the denominator equal to zero. Any horizontal asymptotes are found by looking at what happens when x gets very large or very negative. Draw both the vertical and horizontal asymptotes on your graph as dotted lines. These are like boundaries where the graph does not cross.
2. Find the x and y intercepts. You get the y-intercept by plugging in x = 0. You get the x-intercepts by setting the numerator equal to zero and solving for x. Plot these points on the graph.
3. Select a few key values of x to plug into the function and find the associated y values. You can decide what these are by looking at 1) and 2) above and picking points that help you determine the shape of the graph. Plot these points on your graph.
4. Use all of the above to sketch in the graph. Remember that the graph will go through the points you have drawn and approach, but never get to, the asymptote lines.