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Bartleby Sitemap - Textbook Solutions

All Textbook Solutions for Precalculus Enhanced with Graphing Utilities

80AYU 81AYU 82AYU 83AYU 84AYU In Problems 81-98, analyze each polynomial function by following Steps 1 through 8 on page 193. f( x )= x 2 ( x+3 )( x+1 )86AYU 87AYU 88AYU 89AYU In Problems 81-98, analyze each polynomial function by following Steps 1 through 8 on page 193. f( x )= x 2 ( x 2 +1 )( x+4 )91AYU In Problems 99-106, analyze each polynomial function f by following Steps 1 through 8 on page 195. f( x )= x 3 0.8 x 2 4.6656x+3.73248 In Problems 99-106, analyze each polynomial function f by following Steps 1 through 8 on page 195. f( x )= x 3 +2.56 x 2 3.31x+0.89 94AYU 95AYU 96AYU 97AYU 98AYU 99AYU In Problems 107-114, analyze each polynomial function by following Steps 1 through 8 on page 193. f( x )=x x 3 101AYU In Problems 107-114, analyze each polynomial function by following Steps 1 through 8 on page 193. f( x )= x 3 +2 x 2 8x In Problems 107-114, analyze each polynomial function by following Steps 1 through 8 on page 193. f( x )=2 x 4 +12 x 3 8 x 2 48x 104AYU 105AYU In Problems 107-114, analyze each polynomial function by following Steps 1 through 8 on page 193. f( x )= x 5 +5 x 4 +4 x 3 20 x 2 107AYU 108AYU 109AYU In Problems 115-118, construct a polynomial function f with the given characteristics. Zeros:4( multiplicity1 );0( multiplicity3 );2( multiplicity1 );degree5;containsthepoint( 2,64 )G( x )= (x+3) 2 (x2) a. Identify the x-intercepts of the graph of G . b. What are the x-intercepts of the graph of y=G( x+3 ) ?h( x )=( x+2 ) ( x4 ) 3 a. Identify the x-intercepts of the graph of h . b. What are the x-intercepts of the graph of y=h( x2 ) ?113AYU 114AYU 115AYU h( x )=( x+2 ) ( x4 ) 3 a. Identify the x-intercepts of the graph of h . b. What are the x-intercepts of the graph of y=h( x2 ) ?117AYU 118AYU Write a few paragraphs that provide a general strategy for graphing a polynomial function. Be sure to mention the following: degree, intercepts, end behavior, and turning points.120AYU Make up two polynomials, not of the same degree, with the following characteristics: crosses the x-axis at 2 , touches the x-axis at 1, and is above the x-axis between 2 and 1. Give your polynomials to a fellow classmate and ask for a written critique.Which of the following statements are true regarding the graph of the cubic polynomial f( x )= x 3 +b x 2 +cx+d ? (Give reasons for your conclusions.) a. It intersects the y-axis in one and only one point. b. It intersects the x-axis in at most three points. c. It intersects the x-axis at least once. d. For | x | very large, it behaves like the graph of y= x 3 . e. It is symmetric with respect to the origin. f. It passes through the origin.Which of the following statements are true regarding the graph of the cubic polynomial f( x )= x 3 +b x 2 +cx+d ? (Give reasons for your conclusions.) a. It intersects the y-axis in one and only one point. b. It intersects the x-axis in at most three points. c. It intersects the x-axis at least once. d. For | x | very large, it behaves like the graph of y= x 3 . e. It is symmetric with respect to the origin. f. It passes through the origin.The illustration shows the graph of a polynomial function. a. Is the degree of the polynomial even or odd? b. Is the leading coefficient positive or negative? c. Is the function even, odd, or neither? d. Why is x 2 necessarily a factor of the polynomial? e. What is the minimum degree of the polynomial? f. Formulate five different polynomials whose graphs could look like the one shown. Compare yours to those of other students. What similarities do you see? What differences?125AYU 126AYU 1. Find f( 1 ) if f( x )=2 x 2 x 2. Factor the expression 6 x 2 +x-2 3. Find the quotient and remainder if 3 x 4 -5 x 3 +7x4 is divided by x3 . (pp. A25-A27 or A31-A34)4AYU 5. f( x )=q(x)g( x )+r(x) , the function r( x ) is called the ______ . (a) remainder(b) dividend(c) quotient(d) divisor 6. When a polynomial function f is divided by x-c , the remainder is _______ .7. Given f( x )=3 x 4 -2 x 3 +7x-2 , how many sign changes are there in the coefficients of f( x ) ? (a) 0(b) 1(c) 2(d) 3 8. True or False Every polynomial function of degree 3 with real coefficients has exactly three real zeros.9. If f is a polynomial function and x4 is a factor of f, then f( 4 )= _______.10. True or False If f is a polynomial function of degree 4 and if f( 2 )=5 , then f( x ) x-2 =p( x )+ 5 x-2 where p( x ) is a polynomial function of degree 3.In Problems 11-20, use the Remainder Theorem to find the remainder when f( x ) is divided by x-c . Then use the Factor Theorem to determine whether x-c is a factor of f( x ) . 11. f( x )=4 x 3 -3 x 2 -8x+4 ; x-2 In Problems 11-20, use the Remainder Theorem to find the remainder when f( x ) is divided by x-c . Then use the Factor Theorem to determine whether x-c is a factor of f( x ) . 12. f( x )=-4 x 3 +5 x 2 +8 ; x+3 In Problems 11-20, use the Remainder Theorem to find the remainder when f( x ) is divided by x-c . Then use the Factor Theorem to determine whether x-c is a factor of f( x ) . 13. f( x )=3 x 4 -6 x 3 -5x+10 ; x-2 In Problems 11-20, use the Remainder Theorem to find the remainder when f( x ) is divided by x-c . Then use the Factor Theorem to determine whether x-c is a factor of f( x ) . 14. f( x )=4 x 4 -15 x 2 -4 ; x-2 In Problems 11-20, use the Remainder Theorem to find the remainder when f( x ) is divided by x-c . Then use the Factor Theorem to determine whether x-c is a factor of f( x ) . 15. f( x )=3 x 6 +82 x 3 +27 ; x+3 In Problems 11-20, use the Remainder Theorem to find the remainder when f( x ) is divided by x-c . Then use the Factor Theorem to determine whether x-c is a factor of f( x ) . 16. f( x )=2 x 6 -18 x 4 + x 2 -9 ; x+3 17AYU In Problems 11-20, use the Remainder Theorem to find the remainder when f( x ) is divided by x-c . Then use the Factor Theorem to determine whether x-c is a factor of f( x ) . 18. f( x )= x 6 -16 x 4 + x 2 ; x+4 In Problems 11-20, use the Remainder Theorem to find the remainder when f( x ) is divided by x-c . Then use the Factor Theorem to determine whether x-c is a factor of f( x ) . 19. f( x )=2 x 4 - x 3 +2x-1 ; x- 1 2 In Problems 11-20, use the Remainder Theorem to find the remainder when f( x ) is divided by x-c . Then use the Factor Theorem to determine whether x-c is a factor of f( x ) . 20. f( x )=3 x 4 + x 3 -3x+1 ; x+ 1 3 21AYU In Problems 33-44, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros. 34. f( x )= x 5 - x 4 +2 x 2 +3 In Problems 33-44, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros. 35. f( x )= x 5 -6 x 2 +9x-3 In Problems 33-44, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros. 36. f( x )=2 x 5 - x 4 - x 2 +1 25AYU In Problems 33-44, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros. 38. f( x )=6 x 4 - x 2 +2 In Problems 33-44, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros. 39. f( x )=6 x 4 - x 2 +9 In Problems 33-44, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros. 40. f( x )=-4 x 3 + x 2 +x+6 In Problems 33-44, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros. 41. f( x )=2 x 5 - x 3 +2 x 2 +12 In Problems 33-44, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros. 42. f( x )=3 x 5 - x 2 +2x+18 In Problems 33-44, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros. 43. f( x )=6 x 4 +2 x 3 - x 2 +20 In Problems 33-44, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros. 44. f( x )=-6 x 3 - x 2 +x+10 In Problems 45-50, find the bounds to the zeros of each polynomial function. Use the bounds to obtain a complete graph of f . 45. f( x )=2 x 3 + x 2 -1 In Problems 45-50, find the bounds to the zeros of each polynomial function. Use the bounds to obtain a complete graph of f . 46. f( x )=3 x 3 -2 x 2 +x+4 In Problems 45-50, find the bounds to the zeros of each polynomial function. Use the bounds to obtain a complete graph of f . 47. f( x )= x 3 -5 x 2 -11x+11 In Problems 45-50, find the bounds to the zeros of each polynomial function. Use the bounds to obtain a complete graph of f . 48. f( x )=2 x 3 - x 2 -11x-6 In Problems 45-50, find the bounds to the zeros of each polynomial function. Use the bounds to obtain a complete graph of f . 49. f( x )= x 4 +3 x 3 -5 x 2 +9 In Problems 45-50, find the bounds to the zeros of each polynomial function. Use the bounds to obtain a complete graph of f . 50. f( x )=4 x 4 -12 x 3 +27 x 2 -54x+81 In Problems 51-68, find the real zeros of f. Use the real zeros to factor f 51. f( x )= x 3 +2 x 2 -5x-6 In Problems 51-68, find the real zeros of f. Use the real zeros to factor f 52. f( x )= x 3 +8 x 2 +11x-20 In Problems 51-68, find the real zeros of f. Use the real zeros to factor f 53. f( x )=2 x 3 -13 x 2 +24x-9 In Problems 51-68, find the real zeros of f. Use the real zeros to factor f 54. f( x )=2 x 3 -5 x 2 -4x+12 In Problems 51-68, find the real zeros of f. Use the real zeros to factor f 55. f( x )=3 x 3 +4 x 2 +4x+1 In Problems 51-68, find the real zeros of f. Use the real zeros to factor f 56. f( x )=3 x 3 -7 x 2 +12x-28 In Problems 51-68, find the real zeros of f. Use the real zeros to factor f 57. f( x )= x 3 -10 x 2 +28x-16 In Problems 51-68, find the real zeros of f. Use the real zeros to factor f 58. f( x )= x 3 +6 x 2 +6x-4 In Problems 51-68, find the real zeros of f. Use the real zeros to factor f 59. f( x )= x 4 + x 3 -3 x 2 -x+2 48AYU 49AYU 50AYU In Problems 51-68, find the real zeros of f . Use the real zeros to factor f . f( x )= x 3 -8 x 2 +17x-6 52AYU In Problems 51-68, find the real zeros of f . Use the real zeros to factor f . f( x )=4 x 4 +7 x 2 -2 54AYU 55AYU 56AYU In Problems 69-74, find the real zeros of f . If necessary, round to two decimal places. f( x )= x 3 +3.2 x 2 16.83x5.31 In Problems 69-74, find the real zeros of f . If necessary, round to two decimal places. f( x )= x 3 +3.2 x 2 7.25x6.3 In Problems 69-74, find the real zeros of f . If necessary, round to two decimal places. f( x )= x 4 1.4 x 3 33.71 x 2 +23.94x+292.41 60AYU 61AYU 62AYU In Problems 75-84, find the real solutions of each equation. x 4 - x 3 +2 x 2 -4x-8=0 In Problems 75-84, find the real solutions of each equation. 2 x 3 +3 x 2 +2x+3=0 In Problems 75-84, find the real solutions of each equation. 3 x 3 +4 x 2 -7x+2=0 66AYU 67AYU 68AYU 69AYU 70AYU 71AYU 72AYU 73AYU 74AYU 75AYU 76AYU 77AYU 78AYU In Problems 91-98, analyze each polynomial function using Steps 1 through 8 on page 193 in Section 4.1. f( x )= x 3 +2 x 2 5x6 [Hint: See Problem 51.]In Problems 91-98, analyze each polynomial function using Steps 1 through 8 on page 193 in Section 4.1. f( x )= x 3 +8 x 2 +11x20 [Hint: See Problem 52.]In Problems 91-98, analyze each polynomial function using Steps 1 through 8 on page 193 in Section 4.1. f( x )= x 4 + x 3 3 x 2 x+2 [Hint: See Problem 59.]In Problems 91-98, analyze each polynomial function using Steps 1 through 8 on page 193 in Section 4.1. f( x )= x 4 x 3 6 x 2 +4x+8 [Hint: See Problem 60.]In Problems 91-98, analyze each polynomial function using Steps 1 through 8 on page 193 in Section 4.1. f( x )=4 x 5 8 x 4 x+2 [Hint: See Problem 67.]In Problems 91-98, analyze each polynomial function using Steps 1 through 8 on page 193 in Section 4.1. f( x )=4 x 5 +12 x 4 x3 [Hint: See Problem 68.]In Problems 91-98, analyze each polynomial function using Steps 1 through 8 on page 193 in Section 4.1. f( x )=6 x 4 37 x 3 +58 x 2 +3x18 In Problems 91-98, analyze each polynomial function using Steps 1 through 8 on page 193 in Section 4.1. f( x )=20 x 4 +73 x 3 +46 x 2 52x24 Find k such that f( x )= x 3 k x 2 +kx+2 has the factor x2 .Find k such that f( x )= x 4 k x 3 +k x 2 +1 has the factor x+2 .89AYU 90AYU 91AYU 92AYU 93AYU 94AYU 95AYU 96AYU Let f( x ) be a polynomial function whose coefficients are integers. Suppose that r is a real zero of f and that the leading coefficient of f is 1. Use the Rational Zeros Theorem to show that r is either an integer or an irrational number.98AYU 99AYU 100AYU 101AYU 102AYU Is 2 3 a zero of f( x )= x 7 +6 x 5 x 4 +x+2 ? Explain?1. Find the sum and the product of the complex numbers 32i and 3+5i . (pp. A58-A61)2AYU 3. Every polynomial function of odd degree with real coefficients has at least _____ real zero(s).4. If 3+4i is a zero of a polynomial function of degree 5 with real coefficients, then so is ________.5AYU 6AYU In Problems 7-16, information is given about a polynomial function f( x ) whose coefficients are real numbers. Find the remaining zeros of f . 7. Degree 3; zeros: 3, 4i In Problems 7-16, information is given about a polynomial function f( x ) whose coefficients are real numbers. Find the remaining zeros of f . 8. Degree 3; zeros: 4, 3+i In Problems 7-16, information is given about a polynomial function f( x ) whose coefficients are real numbers. Find the remaining zeros of f . 9. Degree 4; zeros: i , 1+i In Problems 7-16, information is given about a polynomial function f( x ) whose coefficients are real numbers. Find the remaining zeros of f . 10. Degree 4; zeros: 1, 2, 2+i 11AYU 12AYU 13AYU 14AYU 15AYU 16AYU In Problems 17-22, form a polynomial function f( x ) with real coefficients having the given degree and zeros. Answers will vary depending on the choice of the leading coefficient. Use a graphing utility to graph the function and verify the result. Degree 4; zeros: 3+2i ; 4, multiplicity 2 18AYU In Problems 17-22, form a polynomial function f( x ) with real coefficients having the given degree and zeros. Answers will vary depending on the choice of the leading coefficient. Use a graphing utility to graph the function and verify the result. Degree 5; zeros: 2; i ; 1+i In Problems 17-22, form a polynomial function f( x ) with real coefficients having the given degree and zeros. Answers will vary depending on the choice of the leading coefficient. Use a graphing utility to graph the function and verify the result. Degree 6; zeros: i ; 4i ; 2+i In Problems 17-22, form a polynomial function f( x ) with real coefficients having the given degree and zeros. Answers will vary depending on the choice of the leading coefficient. Use a graphing utility to graph the function and verify the result. Degree 4; zeros: 3; multiplicity 2; i In Problems 17-22, form a polynomial function f( x ) with real coefficients having the given degree and zeros. Answers will vary depending on the choice of the leading coefficient. Use a graphing utility to graph the function and verify the result. Degree 5; zeros: 1; multiplicity 3; 1+i In Problems 23-30, use the given zero to find the remaining zeros of each function. f( x )= x 3 4 x 2 +4x16 ; zero: 2i In Problems 23-30, use the given zero to find the remaining zeros of each function. g( x )= x 3 +3 x 2 +25x+75 ; zero: 5i 25AYU In Problems 23-30, use the given zero to find the remaining zeros of each function. h( x )=3 x 4 +5 x 3 +25 x 2 +45x18 ; zero: 3i In Problems 23-30, use the given zero to find the remaining zeros of each function. h( x )= x 4 9 x 3 +21 x 2 +21x130 ; zero: 32i In Problems 23-30, use the given zero to find the remaining zeros of each function. f( x )= x 4 7 x 3 +14 x 2 38x60 ; zero: 1+3i In Problems 23-30, use the given zero to find the remaining zeros of each function. h( x )=3 x 5 +2 x 4 +15 x 3 +10 x 2 528x352 ; zero: 4i In Problems 23-30, use the given zero to find the remaining zeros of each function. g( x )=2 x 5 3 x 4 5 x 3 15 x 2 207x+108 ; zero: 3i In Problems 31-40, find the complex zeros of each polynomial function. Write f in factored form. f( x )= x 3 1 32AYU In Problems 31-40, find the complex zeros of each polynomial function. Write f in factored form. f( x )= x 3 8 x 2 +25x26 34AYU 35AYU 36AYU 37AYU In Problems 31-40, find the complex zeros of each polynomial function. Write f in factored form. f( x )= x 4 +3 x 3 19 x 2 +27x252 39AYU 40AYU 41AYU 42AYU 43AYU 44AYU True or False The quotient of two polynomial expressions is a rational expression, (p. A35)What are the quotient and remainder when 3 x 4 x 2 is divided by x 3 x 2 +1 . (pp. A25- A27)3AYU Graph y=2 ( x+1 ) 2 3 using transformations.(pp.106-114)True or False The domain of every rational function is the set of all real numbers.If, as x or as x , the values of R( x ) approach some fixed number L , then the line y=L is a _____ of the graph of R .If, as x approaches some number c , the values of | R( x ) | , then the line x=c is a ______ of the graph of R .For a rational function R , if the degree of the numerator is less than the degree of the denominator, then R is _____.True or False The graph of a rational function may intersect a horizontal asymptote.True or False The graph of a rational function may intersect a vertical asymptote.If a rational function is proper, then _____ is a horizontal asymptote.True or False If the degree of the numerator of a rational function equals the degree of the denominator, then the ratio of the leading coefficients gives rise to the horizontal asymptote.If R( x )= p( x ) q( x ) is a rational function and if p and q have no common factors, then R is ________. a. improper b. proper c. undefined d. in lowest terms Which type of asymptote, when it occurs, describes the behavior of a graph when x is close to some number? a. vertical b. horizontal c. oblique d. all of these In Problems 15-26, find the domain of each rational function R( x )= 4x x3 In Problems 15-26, find the domain of each rational function R( x )= 5 x 2 3+x In Problems 15-26, find the domain of each rational function H( x )= 4 x 2 ( x2 )( x+4 )In Problems 15-26, find the domain of each rational function G( x )= 6 ( x+3 )( 4x )In Problems 15-26, find the domain of each rational function F( x )= 3x(x1) 2 x 2 5x3 In Problems 15-26, find the domain of each rational function Q( x )= x(1x) 3 x 2 +5x2 In Problems 15-26, find the domain of each rational function R( x )= x x 3 8 In Problems 15-26, find the domain of each rational function R( x )= x x 4 1 In Problems 15-26, find the domain of each rational function H( x )= 3 x 2 +x x 2 +4 In Problems 15-26, find the domain of each rational function G( x )= x3 x 4 +1 25AYU 26AYU 27AYU 28AYU 29AYU 30AYU In Problems 27-32, use the graph shown to find a. The domain and range of each function b. The intercepts, if any c. Horizontal asymptotes, if any d. Vertical asymptotes, if any e. Oblique asymptotes, if any 32AYU In Problems 33-44, (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. F( x )=2+ 1 x In Problems 33-44, (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. Q( x )=3+ 1 x 2 In Problems 33-44, (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. R(x)= 1 ( x1 ) 2 In Problems 33-44, (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. R( x )= 3 x In Problems 33-44, (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. H( x )= 2 x+1 In Problems 33-44, (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. G( x )= 2 (x+2) 2 In Problems 33-44, (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. R( x )= 1 x 2 +4x+4 In Problems 33-44, (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. R( x )= 1 x1 +1 In Problems 33-44, (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. G( x )=1+ 2 (x3) 2 In Problems 33-44, (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. F( x )=2 1 x+1 In Problems 33-44, (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. R( x )= x 2 4 x 2 In Problems 33-44, (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. R( x )= x4 x In Problems 45-56, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. R( x )= 3x x+4 In Problems 45-56, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. R( x )= 3x+5 x-6 In Problems 45-56, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. H( x )= x 3 -8 x 2 -5x+6 In Problems 45-56, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. G( x )= x 3 +1 x 2 -5x-14 In Problems 45-56, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. T( x )= x 3 x 4 -1 In Problems 45-56, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. P( x )= 4 x 2 x 3 -1 In Problems 45-56, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. Q( x )= 2 x 2 -5x-12 3 x 2 -11x-4 In Problems 45-56, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. F( x )= x 2 +6x+5 2 x 2 +7x+5 In Problems 45-56, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. R( x )= 6 x 2 +7x-5 3x+5 54AYU 55AYU 56AYU 57AYU 58AYU Resistance in Parallel Circuits From Ohmâ€™s Law for circuits, it follows that the total resistance R tot of two components hooked in parallel is given by the equation R tot = R 1 R 2 R 1 + R 2 where R 1 and R 2 are the individual resistances. a. Let ohms, and graph R tot as a function of R 2 . b. Find and interpret any asymptotes of the graph obtained in part (a). c. If R 2 =2 R 1 , what value of R1 will yield an R tot of 17 ohms?Newtonâ€™s Method In calculus you will learn that if P( x )= a n x n + a n1 x n1 +...+ a 1 x+ a 0 is a polynomial function, then the derivative of is P ( x )=n a n x n1 +( n1 ) a n1 x n2 +...+2 a 2 x+ a 1 Newtonâ€™s Method is an efficient method for approximating the x-intercepts (or real zeros) of a function, such as p( x ) . The following steps outline Newtonâ€™s Method. STEP 1: Select an initial value x 0 that is somewhat close to the x-intercept being sought. STEP 2: Find values for x using the relation x n+1 = x n P( x n ) P( x n ) n=1,2,... until you get two consecutive values x n and x n+1 that agree to whatever decimal place accuracy you desire. STEP 3: The approximate zero will be x n+1 . Consider the polynomial P( x )= x 3 7x40 . a. Evaluate p( 5 ) and p( 3 ) . b. What might we conclude about a zero of p ? Explain. c. Use Newtonâ€™s Method to approximate an x-intercept , r , 3r5 , of p( x ) to four decimal places. d. Use a graphing utility to graph p( x ) and verify your answer in part . e. Using a graphing utility, evaluate p( r ) to verify your result.61AYU 62AYU 1AYU 2AYU The graph of a rational function cannot have both a horizontal and an oblique asymptote. Explain why.4AYU 5AYU 6AYU 7AYU 8AYU True or False The quotient of two polynomial expressions is a rational expression. (p. A35)True or False Every rational function has at least one asymptote.Which type of asymptote will never intersect the graph of a rational function? (a) horizontal (b) oblique (c) vertical (d) all of these True or False The graph of a rational function sometimes has a hole.In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= x+1 x( x+4 )In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= x ( x1 )( x+2 )In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= 3x+3 2x+4 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= 2x+4 x1 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= 3 x 2 4 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= 6 x 2 x6 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. P( x )= x 4 + x 2 +1 x 2 1 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. Q( x )= x 4 1 x 2 4 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. H( x )= x 3 1 x 2 9 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. G( x )= x 3 +1 x 2 +2x In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= x 2 x 2 +x6 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= x 2 +x12 x 2 4 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. G( x )= x x 2 4 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. G( x )= 3x x 2 1 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= 3 ( x1 )( x 2 4 )In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= 4 ( x+1 )( x 2 9 )In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. H( x )= x 2 1 x 4 16 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. H( x )= x 2 +4 x 4 1 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. F( x )= x 2 3x4 x+2 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. F( x )= x 2 +3x+2 x1 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= x 2 +x12 x4 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= x 2 x12 x+5 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. F( x )= x 2 +x12 x+2 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. G( x )= x 2 x12 x+1 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= x ( x1 ) 2 ( x+3 ) 3 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= ( x1 )( x+2 )( x3 ) x ( x4 ) 2 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= x 2 +x12 x 2 x6 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= x 2 +3x10 x 2 +8x+15 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= 6 x 2 7x3 2 x 2 7x+6 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= 8 x 2 +26x+15 2 x 2 x15 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= x 2 +5x+6 x+3 In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= x 2 +x30 x+6

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