An example of inverse variation from the real world.
Vocabulary for Inverse Variation Graphing
Key terms for graphs involving inverse variation.
Helpful Hints
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.
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.
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.
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.
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.
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
Summary of the findings from Example One and Example Two
