Question

Graph the system of inequalities.

Answer 1

Step 1:

The system of inequalities are

 

Graph the each inequality .

The inequality .

Write the related equation is and it represents a rational function.

The graph of the equation is the boundary of the region. Since the inequality symbol is , the

boundary is drawn as a solid curve to show that points on the curve satisfy the inequality and the

shaded region of the graph of is the solutions to the inequality.

To graph the boundary curve make the table of values to find ordered pairs that satisfy the equation.

Choose random values for and find the corresponding values for .

		Undefined

 

Answer 2

Contd...

The inequality

Write the related equation is and it represents a parabola.

The graph of the equation is the boundary of the region. Since the inequality symbol is ,

the boundary is drawn as a solid curve to show that points on the curve satisfy the inequality and the

shaded region of the graph of is the solutions to the inequality.

To graph the boundary curve make the table of values to find ordered pairs that satisfy the equation.

Choose random values for and find the corresponding values for .

 

Answer 3

Contd..

Step 2:

Graph:

1. Draw a coordinate plane.

2. Plot the points of and draw a smooth curves through these points.

3. To determine which side (out side or in side) to be shaded, use a test point .

Substitute the value of in the original inequality.

Since the above statement is false, shade the region does not contain point .

4. Plot the points of and draw a smooth curve through these points.

5. To determine which side (out side or in side) to be shaded, use a test point inside the parabola. A simple choice is .

Substitute the value of in the original inequality.

Since the above statement is true, shade the region inside the parabola.

Observe the graph: intersection part is solution of the system of linear inequalities:

Solution:

.