Explore: Graphing Systems of Non-Linear Inequalities Solutions - Demme Learning

Graphing Systems of Non-Linear Inequalities Solutions

When given a system of non-linear inequalities remember to determine:
- the type of graph (parent graph)
- a, h, k and any other characteristics unique to the graph
- solid/dashed curves (open/closed points)
- the solution region
The solution is where the shaded regions of all inequalities in the system overlap .
If there is no overlapping region, you must write “no solution” on or under the graph to note there is no ordered pair that will make all of the inequalities true.

Example 4

Graph the system of inequalities.

$y > |x + 2| y \leq \sqrt{x + 3} - 2$

This system has no solution because there are no shared ordered pairs in the shaded regions.

Note

Saying your plan out loud may be helpful in getting started.

Remember that square root equations and inequalities have a vertical asymptote and this restricts the solutions.

Use a test point if your are not sure where to shade. The ordered pair must be true for every inequality in the system.

no solution

Example 5

Graph the system of inequalities.

$y \geq - |x - 3| - 1 y \leq |x - 4| - 4$

Example 6

Graph the system of inequalities.

$y > \frac{1}{x} y < - \frac{1}{x}$

Example 7

Graph the system of inequalities.

$y \geq {(x - 2)}^{3} + 1 y < \sqrt[3]{x - 1} + 2$

Note

All of these graphs can also be checked using technology.