1. January 25, 2012 At the end of today, you will be able to solve polynomial and rational inequalities. Warm-up: Correct HW 2.6: 29. D: all reals, x≠-2; y-int: (0, -1/2); VA: x=-2; HA: y = 0 31. D: all reals, x≠-1; xint: (-5/2,0; yint: (0,5); VA: x = -1; HA: y = 2 33. D: all reals; x-yint: (0,0); HA y = 1 35. D: all reals; x-yint: (0,0): HA y = 0 37. D: all reals, x ≠ ±2; xint: (1, 0); yint: (0, -1); VA: x = ±2; HA: y = 1 39. D: all reals, x ≠ ±1, 2; xint: (3, 0), (-1/2,0); yint: (0, -3/2); VA: x = 1, x = ±1; HA: y = 0 55. D: all reals, x±0; no intercepts; VA: x = 0; Slant: y = x 57. D: all reals, t≠-5; yint: (0, -0.2); VA: t = -5; Slant: y = -t + 5 TEST THURSDAY 2/02

2. Lesson 2.7 Non-Linear Inequalities Example 1: Solving a Polynomial Inequality x 2 – 6x + 9 < 16 x 2 – 6x – 7 < 0 (x – 7)(x + 1) < 0 Critical numbers: x = 7 and x = -1 1. Set the polynomial to 0. 2. Factor and find the zeros (critical numbers) 3. Make number line and set up test intervals to find solution. 0 7 Test Interval (-∞, -1) (-1, 7) (7, ∞) Test Value Equals < 0? x = -2 (-2) 2 – 6(-2) - 7 x = 0 (0) 2 – 6(0) - 7 x = 8 (8) 2 – 6(8) - 7 9 No -7 Yes 9 No (-1, 7)

3. Test intervals are most useful to find the domain of a square root of polynomial Example 2: Find the domain of 1. Set the polynomial to 0. 2. Factor and find the zeros (critical numbers) 3. Make number line and set up test intervals to find solution. Test Interval Test Value Equals ≥ 0 ?

4. Rational Inequalities Example 3: 1. Set the polynomial to 0. 3. Find zero and undefined values 4. Make number line and set up test intervals to find solution. 2. Find the least common denominator and combine. Test Interval Test Value Equals ≤ 0 ? (-∞, 5)(5, 8)(8, ∞)

5. Classwork 2.7 Pg. 204 #15, 16, 21, 24, 38, 42, 57, 58 #15-24 Solve and graph on a number line 15. x 2 + x 3 21. x 3 – 3x 2 – x + 3 > 0 24. 2x 3 + 13x 2 – 8x – 46 ≥ 6 38. 40. Find the domain of x and graph in calculator to verify. 57. 58.

6. Unit 5 Review: Pg. 208 #7, 21, 31, 33, 47, 61, 63, 73, 75, 103, 105, 121, 129, 131, 139, 141 What to know for the test… Using the maximum, minimum and zeros of a quadratic in word problems. Analyzing the behavior of a polynomial function – inc, dec, multiplicity, turning point Finding the zeros of a polynomial, using division. Adding, subtracting, multiplying and dividing complex number. Finding the domain and asymptotes of rational functions Finding solutions of polynomial and rational inequalities. Additional things to remember: Trig functions