AN20 Answers: Chapter 4 5. Step 1: = y x3 Step 2: x-intercepts: 0, 3; y-intercept: 0 Step 3: 0: multiplicity 2; touches; 3: multiplicity 1; crosses Step 4: 10 22 210 4 Step 5: ( ) ( ) − 2, 4; 0,0 Step 6: y 24 x 5 (4, 16) (3, 0) (0, 0) (2, 24) (21, 24) Step 7: Range: ( ) −∞∞, Step 8: Increasing on ( ] −∞, 0 and [ )∞ 2, Decreasing on [ ] 0, 2 7. Step 1: = − y x3 Step 2: x-intercepts: −4, 1; y-intercept: 16 Step 3: −4: multiplicity 2, touches; 1: multiplicity 1, crosses Step 4: 60 27 260 5 Step 5: ( ) ( ) − − 4, 0 ; 0.67, 18.52 Step 6: y 50 250 x (0, 16) (1, 0) (2, 236) (24, 0) (25, 6) (20.67, 18.52) 26 2 Step 7: Range: ( ) −∞∞, Step 8: Increasing on [ ] − − 4, 0.67 Decreasing on ( ] −∞ −, 4 and [ ) − ∞ 0.67, 9. Step 1: = − y x2 4 Step 2: x-intercepts: −2, 2; y-intercept: 32 Step 3: −2: multiplicity 1, crosses; 2: multiplicity 3, crosses Step 4: 75 23 2100 4 Step 5: ( ) −1, 54 Step 6: y 2240 x 5 (22, 0) (21, 54) (0, 32) (2, 0) (3, 210) (23, 2250) Step 7: Range: ( ] −∞, 54 Step 8: Increasing on ( ] −∞ −, 1 Decreasing on [ ) − ∞1, 4.2 Assess Your Understanding (page 211) 11. Step 1: = y x3 Step 2: x-intercepts: − − 4, 1, 2; y-intercept: −8 Step 3: − − 4, 1, 2: multiplicity 1, crosses Step 4: 15 25 215 5 Step 5: ( ) −2.73, 10.39 ; ( ) − 0.73, 10.39 Step 6: y 50 x 5 (3, 28) (2, 0) (0.73, 210.39) (24, 0) (21, 0) (25, 228) (0, 28) (22.73, 10.39) Step 7: Range: ( ) −∞∞, Step 8: Increasing on ( ] −∞ −, 2.73 and [ )∞ 0.73, Decreasing on [ ] −2.73, 0.73 13. Step 1: = y x3 Step 2: x-intercepts: 0, 1, 2 y-intercept: 0 Step 3: 0, 1, 2: multiplicity 1, crosses Step 4: 24 22 3 4 Step 5: ( ) ( ) − 0.42, 0.38 ; 1.58, 0.38 Step 6: y 5 x 3 (2, 0) (1, 0) (0, 0) (1.58, 20.38) (0.42, 0.38) Step 7: Range: ( ) −∞∞, Step 8: Increasing on ( ] −∞, 0.42 and [ )∞ 1.58, Decreasing on [ ] 0.42, 1.58 15. Step 1: = y x4 Step 2: x-intercepts: −1, 2; y-intercept: 4 Step 3: −1, 2:multiplicity 2, touches Step 4: 10 24 25 4 Step 5: ( ) ( ) ( ) −1, 0 ; 2, 0 ; 0.5, 5.06 Step 6: y 20 x (2, 0) 5 (0.5, 5.06) (0, 4) (21, 0) (3, 16) (22, 16) Step 7: Range: [ )∞ 0, Step 8: Increasing on [ ] −1, 0.5 and [ )∞ 2, Decreasing on ( ] −∞ −, 1 and [ ] 0.5, 2 17. Step 1: = − y x2 4 Step 2: x-intercepts: −4, 1, 4 y-intercept: 32 Step 3: −4, 4: multiplicity 1, crosses; 1: multiplicity 2, touches Step 4: 2100 25 5 250 Step 5: ( ) ( ) ( ) −2.59, 239.51 ; 1, 0 ; 3.09, 56.37 Step 6: y 250 x 5 (1, 0) (4, 0) (0, 32) (22.59, 239.51) (3.09, 56.37) (24, 0) Step 7: Range: ( ] −∞, 239.51 Step 8: Increasing on ( ] −∞ −, 2.59 and [ ) 1, 3.09 Decreasing on [ ] −2.59, 1 and [ )∞ 3.09,
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