1. Warm-up:
Solve the inequality and graph the solution set. x3 + 2x2 – 9x  18
HW: pg (4, 5, 7, 9, 11, 30, 34, 46, 52, 68, 80, 81, 82, 84, 86, 88)

3. Objective:
Check Polynomial Equation solutions with the TI83/84 calculator
Solve and graph rational inequalities.
Write solutions in interval notation.

4. Review Polynomial Inequalities
Solve:
Put in standard form:
Replace the > with an = and solve to get boundaries

5. The solution is x > 2 written in interval notation is
Put the solutions (x = -2 or x = 2) to the equation on a number line to get intervals.
(-, -2) , (-2, 2) , (2, )
Pick a test point in each interval formed and determine if the interval is in the solution.
The solution is x > 2 written in interval notation is

6. TI83/84 Calculator
We can get to the same conclusion using the TI83/84 calculator.
Method:
Put the polynomial equation in standard form
Enter the left side as a function [y=]
Find the zeros
Examine the graph to determine position or negative f(x) values

7. Find the zeroes: x = -2 or x = 2
Examine the graph to see that the positive values occur when x > 2
This is verified in the Table.

8. Solve
Solution:
x3 – 6x2 + 3x + 10 ≤ 0
The solution set is

9. Rational Inequalities
EXAMPLE
Solve and graph the solution set:
SOLUTION
1) Express the inequality so that one side is zero and the other side is a single quotient and simplify!
This inequality is equivalent to the one we wish to solve. It is in
the form f (x) < 0, where

10. Rational Inequalities
2) Set the numerator and the denominator of f equal to zero. The real solutions are the boundary points.
We will use these solutions as boundary points on a number line.
3) Locate the boundary points on a number line and separate the line into intervals.
The boundary points divide the number line into three intervals:

11. Rational Inequalities
4) Choose one representative (test) number within each interval and evaluate f at that number.
Interval
Test Number
Check
Conclusion

12. Rational Inequalities
CONTINUED
5) Write the solution set, selecting the interval(s) that satisfy the given inequality.
The graph of the solution set on a number line is shown as follows: ) (

13. Example: Solve the inequality
Pick a test point for each interval

14. Since this inequality involves equality, we include – 7.
Since (-, 7) and (4, ) are part of the solution we shade the regions.
Since this inequality involves equality, we include – 7.
The point, x = 4, cannot be included since it is a domain restriction!
The solution set is

15. Summary:
Check Polynomial Equation solutions with the TI83/84 calculator
Solve and graph rational inequalities.
Write solutions in interval notation.

16. HW: pg (4, 5, 7, 9, 11, 30, 34, 46, 52, 68, 80, 81, 82, 84, 86, 88)