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How to Graph Polynomial & Rational Functions

Polynomial and rational functions are expressions from which many other functions are derived or represented. The graphs of these functions are often used to teach students the process of manually graphing the data points of an equation. These graphs give insight into the continuity and change of functions over their domain. Graphing of polynomial and rational functions is a procedure that is first encountered in intermediate algebra courses.

Things You'll Need

  • Pencil
  • Paper
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Instructions

    • 1

      Create a small table with two columns and two rows.

    • 2

      Label, from left to right, the cells of the first row "x" and "y."

    • 3

      Insert vertically several values of the domain of the function into the first cell of the second row. The most commonly used values are the natural numbers starting with 1. For example, the first seven values would be the whole numbers 1 through 7.

    • 4

      Evaluate the polynomial or rational function at each value in the second row of the first column. The value returned is placed in the column directly to the right of the value being evaluated.

    • 5

      Plot the points generated by the table. The value in the left column of the second row is the x-coordinate and the value in the right column of the second row is the y-coordinate.

    • 6

      Connect the plotted points with a smooth, continuous curve. The curve generated by this step is the graph of the function.

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