Answers sign-charts
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1. (x - 2)(x + 3) is factorable and greater than or equal to 0 when both factors have the same sign. 2. (x + 3)2 is always greater than or equal to 0. 3. -x(x + 3) is less than or equal to 0 when one factor is positive and one is negative.
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Answers sign-charts
- 1. Answer to Sign–charts of Factorable Functions (x – 2)(x + 3) 2 0 + +– –1. – – –3 + + (x + 3) (2 – x)2 0 + + – ––33. – –x (x + 3) 0 + + – –5. –3 – 0 : where f = 0 (x + 3)2 + +7. –3 0 + + + + – –1/2 3 9. + + – – x (2x – 1)(3 – x) 0 + + – –1/2 3 11. – – x (2x – 1)(3 – x) 0 + +1/2 3 13. x (2x – 1)(3 – x)+ ++ + + + –1 0 3 15. x2 (x – 3)(x + 1)+ + + +– –– – : where f is UDF
- 2. Answer to Sign–charts of Factorable Functions 19. –2 + +3 4+ + – – : where f = 0 : where f is UDF or excluded – – (x – 4)(x + 2) (3 – x) (x – 2)(x + 3) ≥0 2 0 + +21. –3+ + (x + 3) (2 – x)2 0 – ––323. – –x (x + 3) ≤0 0 – –25. –3 – 0 x2 – 4 > 0 27. + +1/2 3 29. + + x (2x – 1)(3 – x) > 0 31. ≤0 (x – 3)(x + 1) > 0 3 0 + +–1 + + 2 0 + +–2 + + 33. 2 0 –3 UDF UDF – – (x + 3) (x – 2)2 ≤0 35. –2 3 4 – –– – (x – 4)(x + 2) (3 – x) ≤0