A rational function is one of the form \(\frac{p(x)}{q(x)}\), where both \(p(x)\) and \(q(x)\) are polynomials. A sketch of these functions can be obtained by finding certain properties, such as intercepts and asymptotes.

This applet can be used to practice sketching rational functions, without tools used in calculus (such as the first and second derivative tests). By following the prompts, you'll collect sufficient information about the function to draw an approximation of its graph.

Enter the required information in the prompts on the right. Note that the \(y\)-intercept must be entered as a point, such as (0, 2) or (0,2). The parentheses and comma should be included, and the order of the numbers in the pair will also be tested. As each correct answer is given, you'll be asked to find the next piece of information about the function. In the last step, you'll click on the plot itself near a point on the graph (some flexibility is provided here - as long as your point is within 0.5 units of the actual graph, your point will be accepted). When enough points are gathered, the actual graph of the function will be drawn.

Enter the required information in the prompts on the right. Note that the \(y\)-intercept must be entered as a point, such as (0, 2) or (0,2). The parentheses and comma should be included, and the order of the numbers in the pair will also be tested. As each correct answer is given, you'll be asked to find the next piece of information about the function. In the last step, you'll click on the plot itself near a point on the graph (some flexibility is provided here - as long as your point is within 0.5 units of the actual graph, your point will be accepted). When enough points are gathered, the actual graph of the function will be drawn.

This applet was created using JavaScript and the Raphael library. If you are unable to see the applet, make sure you have JavaScript enabled in your browser. This applet may not be supported by older browsers.