1. 3.5 Polynomial and Rational Inequalities

2. Solving Equations Let’s review solving the following equation:
(-1.5,0)
(2,0)
*A polynomial function can only change signs at its zeros (x-ints).*

3. Solving Inequalities
Solve the following inequality without graphing:

4. Solving Polynomial Inequalities
What steps did we use to solve ?
1) Get everything on the left side to set equal to zero.
2) Find the zeros of f (x) by factoring.
3) Use zeros to separate real number line into test intervals.
4) Pick value from each test interval to evaluate sign of f (x).
5) Write out solution region in interval notation.

5. Solving Inequalities
Solve the following inequality without graphing:

6. Solving Inequalities
Solve the following inequalities without graphing: 1) 2)

7. Solving Rational Equations
Let’s review solving the following equation:
(-1.25,0)
*A rational function can change signs at its
zeros (x-ints) AND where f is undefined.*

8. Solving Inequalities
Solve the following inequality without graphing:

9. Solving Rational Inequalities
What steps did we use to solve rational inequalities?
1) Get everything on the left side and zero on the other.
2) Find the zeros AND where f (x) DNE by finding common denominator.
3) Use these to separate real number line into test intervals.
4) Pick value from each test interval to evaluate sign of f (x).
5) Write out solution region in interval notation.

10. 3.5 Polynomial and Rational Inequalities
Homework #3:
Page 217
#11, 17, 23, 33 – 37 Odd, 43