Graphing Inverse Variation Functions

Graphing Inverse Variation Functions

Author: Alex G

After completing this packet you will be able to:
*sketch a graph of a function in which y varies inversely as x.
*draw your sketch by hand without using a graphing calculator.
*draw both branches of the hyperbola.
*identify the vertical and horizontal asymptotes of the function.
*identify the domain and range of an inverse variation function

The packet contains instructional videos about inverse variation graphing, including two example problems, as well as a slide show of relevent vocabulary. The packet also includes a set of helpful hints to get you through inverse variation graphing problems.

Cover art of field of hay was taken from the Morgue File http://www.morguefile.com website which grants permission for use of its images.

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An example of inverse variation from the real world.

Vocabulary for Inverse Variation Graphing

Key terms for graphs involving inverse variation.

Helpful Hints

  1. Remember that your hyperbola should have two branches.   Unless the domain of the inverse variation problem you are graphing is only positive numbers, remember to use both positive and negative values for x.
  2. You can't divide by zero.  If the x-value you are using causes you to divide by zero, then the y-coordinate is undefined.   Use some x-values on both sides of that value to figure out the behavior of the function near that point.  The x-value that results in trying to divide by zero represents the location of the vertical asymptote.
  3. Use some fractions in your table.  You will be able to see the behavior of the function near the vertical asymptote more easily if you use some fractions.
  4. Use some big numbers in your table.  You will be able to see the behavior of the function as x gets very positive or very negative more easily if you try some larger values for x.
  5. Exclude the x-value of the vertical asymptote from the domain.  The domain of a hyperbola is all real numbers except for real numbers that cause you to divide by zero.
  6. Exclude the y-value of the horizontal asymptote from the range.  Because the hyperbola never reaches its limiting value, the range of a hyperbola is all real numbers except for the limiting value of the function.

Example One

One example problem of graphing inverse variation y = 2/x


Summary of the findings from Example One and Example Two

Example Two

Goes through the steps to graph y = -3/x