FDWKCalcSM_ch1

FDWKCalcSM_ch1 - Section 1.1 Chapter 1 Prerequisites for...

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Section 1.1 1 Chapter 1 Prerequisites for Calculus Quick Review 1.1 1. y = 2 + 4(3 3) = 2 + 4(0) = 2 + 0 = 2 2. 3=3 2( +1) 3=3 2 2 2=2 =1 −− x x x x 3. m = = =− 23 54 1 1 1 4. m = = 31 5 4 () 5. (a) 32 4 1 4 5 615 ? = −= Yes (b) 33 4 1 5 13 5 ( ) ? −−= No 6. (a) 72 1 5 725 = −−+ =+ ? (b) 12 25 19 + 7. dx x y y + + = 21 2 2 22 01 10 2 8. x y y + =−+ ( 2 2 2 2 1 3 1 1 ) 2 2 4 3 1 16 9 25 9 5 3 +− = = 9. 437 34 7 4 3 7 3 xy yx −+ 10. −+ = 25 3 523 2 5 3 5 Section 1.1 Exercises 1. Δ=−−=− Δ=−− =− x y 11 2 12 3 2. Δ=−−− = x y 13 2 22 4 3. Δ=−−− =− Δ=−= x y 835 11 0 4. x y 000 24 6 5. (a, c) y B A x 5 5 (b) m = == 3 1 3 6. (a, c) (b) m = −−− = 1 3 1 3 7. (a, c) y BA x 5 5 (b) m = = = 0 3 0 Section 1.1 Lines (pp. 2–11)
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2 Section 1.1 8. (a, c) (b) m = −− = 32 11 5 0 (undefined) This line has no slope. 9. (a) x = 3 (b) y = 2 10. (a) x = 1 (b) y = 4 3 11. (a) x = 0 (b) y =− 2 12. (a) x = ± (b) y = 0 13. y = 1( x 1) + 1 14. yx − − + + + 1 1 [( ) ] () 15. y = 2( x 0) + 3 16. + + + 24 0 0 [() ] 17. y = 3 x 2 18. y = 1 x + 2 or y = x + 2 19. 1 2 3 20. 1 3 1 21. m xy = = + = = −= 30 20 3 2 3 2 00 3 2 23 320 22. m y = == + = 21 0 1 0 01 1 1 23. m = −−− = 22 2 0 (undefined) Vertical line: x = 2 24. m = = + + 3 4 3 4 3 4 43 ) ] (24 2 34 2 ) + += 25. The line contains (0, 0) and (10, 25). m = = 25 0 10 0 25 10 5 2 5 2 26. The line contains (0, 0) and (5, 2). m = = = 50 2 5 2 5 27. 341 2 1 2 3 4 3 + + (a) Slope: 3 4 (b) y -intercept: 3 (c) [–10, 10] by [–10, 10] 28. =− + 2 2 (a) Slope: 1 (b) y -intercept: 2 (c)
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Section 1.1 3 29. xy yx 34 1 43 1 4 3 4 += =− + + (a) Slope: 4 3 (b) y -intercept: 4 (c) [–10, 10] by [–10, 10] 30. y = 2 x + 4 (a) Slope: 2 (b) y -intercept: 4 (c) 31. (a) The desired line has slope 1 and passes through (0, 0): y = 1( x 0) + 0 or y = x . (b) The desired line has slope = 1 1 1 and passes through (0, 0): y = 1( x 0) + 0 or y = x . 32. (a) The given equation is equivalent to y = 2 x + 4. The desired line has slope 2 and passes through ( 2, 2): y = 2( x + 2) + 2 or y = 2 x 2. (b) The desired line has slope = 1 2 1 2 and passes through ( 2, 2): y x =+ + = + 1 2 22 1 2 3 () o r . 33. (a) The given line is vertical, so we seek a vertical line through ( 2, 4): x = 2. (b) We seek a horizontal line through ( 2, 4): y = 4. 34. (a) The given line is horizontal, so we seek a horizontal line through = 1 1 2 1 2 ,: . y (b) We seek a vertical line through 1 1 2 1 . x 35. m fx x x = = + = 92 31 7 2 7 2 12 7 2 3 2 ( ) Check: f 5 7 2 5 3 2 16 = , as expected. Since x 7 2 3 2 , we have m = 7 2 and b 3 2 . 36. m x x = −−− = + − 41 42 3 2 3 2 3 2 21 3 2 ( ) ( ) + 2 Check: f , 6 3 2 62 7 + as expected. Since x , + 3 2 2 we have m 3 2 and b = 2. 37. −= −− −= − 2 3 3 2 3 63 1 y y y y 38. 2 8 28 4 82 6 = x x x x 39. + =−+ 13 4 1 i This is the same as the equation obtained in Example 5. 40. (a) When y = 0, we have x c = 1, so x = c . When x = 0, we have y d = 1 , so y = d .
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FDWKCalcSM_ch1 - Section 1.1 Chapter 1 Prerequisites for...

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