1. Polynomial and Rational Inequalities
Lesson 4.6

2. Steps for Symbolic Solution
Write as an equation
Solve resulting equation for boundary numbers
Use boundary numbers to separate number line into disjoint intervals
Make a table of test values
One value from each interval
Use this to specify which intervals satisfy the original inequality

3. Example Consider Rewrite as an equation = 0 and graph Determine zeros
Note and test intervals
≤ 0

4. Numeric Solution View table on calculator
Note intervals of x where the function goes above or (in this case) below zero

5. Solving Rational Inequalities
Given an inequality involving a rational function,
As necessary rewrite
Solve p(x) = 0, q(x) = 0
Solutions are boundary numbers
Use boundary numbers to separate number line into disjoint intervals
On intervals is always > 0 or < 0
Use test values to solve original inequality

6. Example Solve Determine intervals which satisfy inequality
2x = 0 when x = 0
(x – 2) = 0 when x = 2
Determine intervals which satisfy inequality
Note function undefined at x = 2
boundary points

7. Assignment
Lesson 4.6
Page 309
Exercises1 – 47 odd