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mac1105_review_3_ans - Answers Review Unit III 1(a x = 1 x...

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Answers – Review Unit III 1. (a) 1 x = − , 5 x = , 2 2 y x = + (b) D: { } 1,2,4 x x ≠ − Symmetry: None Hole: 1 2, 6 VA: 4 x = and 1 x = − HA: 1 y = x -intercepts: 1 x = and 3 x = y -intercept: 3 4 y = − Intercept with HA: ( ) 7,1 2. ( )( ) 2 2 2 3 4 ( ) ( 2) ( 1)( 4) x x x R x x x x + + = + + 3. (a) Domain: { } 0, 2 x x ± \ (b) 3 3 , 2 2 (c) ( ) ( ) 3 , 2 ,0 0,2 2 x ∈ −∞ − ∪ − 4. (c) ( ] ( ) 3, 0 3, +∞ (d) ( , 5) ( 2,1) {6} −∞ − ∪ − 5. { } (1, 3) 6. (a) C (b) A (c) B 7. 1 18 3 mi/hr and 2 1 3 mi/hr 8. Quotient: 2 2 6 22 x x + + , Remainder: 61 9. ( ) 2 153 f = 10. No 11. 5, 2, 2, 3 , 3 i i 12. Zeros are on [ ] 3, 2 , [ ] 1,0 , [ ] 1,2 13. ( ) 3 2 f x x = , ( ) 2 5 3 4 g x x x = + 14. (a) ( )( ) 2 1 x f g x x = Domain: ( ) ( ] ,0 0,1 −∞ ( ) 2 1 1 f x g x x = Domain: ( ) ( ) ,0 0,1 −∞ (b) 1 18 (c) 1 (d) ( ) 1 ( ) 1 f g x x = D Domain: ( ) ,1 −∞ ; ( )( ) 2 1 x g f x x = D Domain: ( ] [ ) , 1 1, −∞ − +∞ 15. f and h
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17. (a) ( ) 1 2 5 1 x f x x + = , Domain: ( ) ( ) ,1 1, −∞ +∞ , Range: ( ) ( ) , 2 2, −∞ − +∞ (b) ( ) 1 1 1 f x x = + + , Domain: [ ) 1, +∞ , Range: [ ) 1, +∞ (c) 1 2 ( ) 1 1 f x x = − + + , Domain: [0, ) +∞ , Range: [0, ) +∞ 18. Domain: ( ) , −∞ +∞ Range: ( ) ,2 −∞
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