How Do You Graph a Function?

How Do You Graph a Function?

To graph a function, create a table containing several ordered pairs, and plot the points on a graph. Depending on the type of function, the number of ordered pairs needed can vary. Use your own discretion when determining how many points are enough.

  1. Pick a point to solve

    Draw a T shape, labeling one side as x and one side as y. Then substitute the value of x into the equation, and solve it to find the corresponding point for y. For example, when given the function y = x^2 - 3x + 2, start by substituting 0. In this example, (0)^2 - 3(0) + 2 is 2. Therefore, the first ordered pair is (0, 2). Write these values in the table.

  2. Solve adjacent values of x

    For simplicity, pick 1 as the next value to plug into x. The example function converts to (1)^2 - 3(1) + 2, or 0. The ordered pair is (1, 0). Going the other way, use -1 as the value. This yields (-1)^2 - 3(-1) + 2, which simplifies to 6 for an ordered pair of (-1, 6). Enter these values into the table as well.

  3. Add two more ordered pairs on either side

    Typically, five values are enough to give you an idea of what the function looks like. For polynomial functions, you might want to add more.

  4. Plot the points on a graph

    Set the origin point at (0, 0). Using the points already identified, plot them on the graph, and draw lines connecting the points.