andim 3-44, (a) graph the rational function using transformations (b) use the final graph to find the domain and rungr, and () e dthe insect i months after being transplanted is iementalists declared the insect endangered and ranplanted the insect into a protected area. The population P h lit any vertical, horizontal, or oblique asymptotes Solve g(h)- 0. How do you interpret your answer? the Amazon Rain Forest. To protect the species hpulation Model A rare species of insect was discovered SECTION 43 Properties of Rational Functions 207 31. 32. (1.-2 \S. R(4) - (x- 1) 34. Q(x) - 3+ 36. R(x) - RFa)-2 -2 2 38. G(x) - -1 sta)- I+1 (x + 2)? 39. R(x)- + 4 +4 40. R(x)- 2. AG) -1+- 3)" 1 42. F(x) - 2- 43. R(x) - 4. R(x) - *+1 lent 45-56, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function 3x + 5 P-8 3x +4 \a. H(x) - 46. R(x)- 7- Sx + 6 48. G(x) - - Sx - 14 la u)- -1 4x 50. P(x) -- 1 2r - S - 12 51. Q(x) - - 11x-4 *+ 6x + 5 52. F(x)-구 + 7u+ 5 2고 + 7x + 5 56. F(x) -- 16 - 2x &r + 26x - 7 6r + 19x - 7 3r-1 55. G(x) - 54. R(x) - 4x-1 Applications and Extensions t Ganity In physics, it is established that the acceleration due pavity, g (in meters/sec"), at a height h meters above sea level is given by (a) How many insects were discovered? In other words what was the population when / 0? (b) What will the population be after 5 years? (c) Determine the horizontal asymptote of P(1). What is the largest population that the protected area can sustain? 3.99 x 104 g(A) = (6.374 x 10 + h) 59. Resistance in Parallel Circuits From Ohm's Law for circuits it follows that the total resistance R of two components hooked in parallel is given by the equation here 6.374 x 10 is the radius of Earth in meters What is the acceleration due to gravity at sea level? The Willis Tower in Chicago, Illinois, is 443 meters tall. What is the acceleration due to gravity at the top of the wills Tower? o The peak of Mount Everest evel. What is the acceleration due to gravity on the peak of Mount Everest? 0 Find the horizontal asymptote of g(h). She g(h) - 0. How do vou interpret your answer? RR; R R.+ R is 8848 meters above sea where R and R: are the individual resistances (a) Let R 10 ohms, and graph R as a function of R. (b) Find and interpret any asymptotes of the graph obtained in part (a). () If R - 2VR, what value of R, will yield an R of 17 ohms? e Amazon Rain Forest. To protect the species e insect months after being transplanted is 50(1 + 0.51) 2+ 001 P(1) -