How Do You Graph Rational Functions?

After setting each variable to zero and solving for the X and Y intercepts, plug in various positive and negative numbers for X and solve the equation to find points in the graph of the function. After finding enough points that lie on the graph of the function, a line can be drawn through the points that will estimate the function's behavior.

When points have been found within the function that have X and Y coordinates, the X coordinate corresponds to where the point lies horizontally on the graph, and the Y coordinate corresponds to where the point lies vertically on the graph.

  1. Find the X and Y intercepts
  2. Substitute X for zero in the function and solve for Y to find the Y intercept. Then, substitute Y for zero and solve for X to find the X intercept.

  3. Find five or six more points on the graph of the function
  4. Set X equal to five or six different numbers, including negative numbers and positive numbers. Solve for each of the corresponding Y values.

  5. Plot the points
  6. Plot all of the points found above onto the graph in the correct corresponding X and Y positions. Then, draw a line through the points to estimate the behavior of the function at all X values.