Algebra II : Graphing Hyperbolic Inequalities

Example Questions

Example Question #1 : Graphing Hyperbolic Inequalities

Which inequality does this graph represent?

Explanation:

The hyperbola in the question's graph is .

This could be discerned because it subtracts from and not the other way around, putting the zeros on the  axis. This narrows the answers down to and .

Test a point to tell which inequality is being used in the graph.

The point  is within the shaded region, for example.

, which is greater than 16, so the answer is .

Example Question #1 : Graphing Hyperbolic Inequalities

Which inequality does this graph represent?

Explanation:

The hyperbola in the graph has y-intercepts rather than x-intercepts, so the equation must be in the form and not the other way around.

The y-intercepts are at 1 and -1, so the correct equation will have just and not .

The answer not must either be,

or .

To see which, test a point in the shaded area.

For example,

, which is less than 1, so the answer is .