
To find: the intercepts and asymptotes, and then sketch a graph of the rational function. To state the domain and range.

Answer to Problem 59E
The function has no
The vertical asymptote occurs at
The equation for the horizontal asymptote is
The domain of the function is equal to
The range of the function is equal to
Explanation of Solution
Given information:
Given function,
Calculation:
Consider the function,
To solve for the
Consider,
Therefore, the function has no
To solve for the
Consider,
Vertical asymptotes:
The vertical asymptote occurs at the point that makes the denominator of the function zero.
The denominator of the function is,
Find the vertical asymptotes,
Therefore, the vertical asymptote occurs at
Horizontal asymptotes:
The degree of the numerator and denominator are the same, the horizontal asymptote occurs at the point determined by the following equation:
The equation for the asymptote is
Sketch the graph of the function
From the graph,
The vertical asymptote at
The domain of the function is equal to
The horizontal asymptote at
The range of the function is equal to
Chapter 3 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- i need help please . and please dont use chat gpt i am trying to learn and see the mistake i did when solving minearrow_forwardi need help please . and please dont use chat gpt i am trying to learn and see the mistake i did when solving minearrow_forwardThe radius of a sphere decreases at a rate of 3 m/s. Find the rate at which the surface area decreases when the radius is 8 m. Answer exactly or round to 2 decimal places. The surface area decreases at a rate of m²/sarrow_forward
- i need help pleasearrow_forward(#1) Consider the solid bounded below by z = x² and above by z = 4-y². If we were to project this solid down onto the xy-plane, you should be able to use algebra to determine the 2D region R in the xy-plane for the purposes of integration. Which ONE of these limite of integration would correctly describe R? (a) y: x24x: -22 - (b) y: 22 x: 04-y² (c) y: -√√4-x2. →√√4x²x: −2 → 2 (d) z: 24-y² y: -2 → 2 (e) None of the abovearrow_forwardX MindTap - Cenxxxx Answered: tat "X A 26308049 X 10 EKU-- SP 25: X E DNA Sequenc X b/ui/evo/index.html?elSBN=9780357038406&id=339416021&snapshotid=877369& GE MINDTAP , Limits, and the Derivative 40. Answer 5 4-5 t-10 5 f(x) = 2x - 4 if x ≤0 if x 0 10 ++ -4-3-2-1 f(x) = MacBook Pro Search or type URL 5 1234 x² +1 if x = 0 if x = 0 +arrow_forward
- MindTap - Cemy X Answered: tat x A 26308049 × 10 EKU--SP 25:11 × E DNA Sequence x H. pylori index.html?elSBN=9780357038406&id=339416021&snapshotid=877369& NDTAP and the Derivative 41. 42. Answer 12 Ay 5 + -10-5 5 10 -5- f(x) = x +5 if x ≤ 0 -x²+5 if x > 0 to -5 5. 5 f(x) = |x − 1| MacBook Pro AAarrow_forwardMind Tap - Cenxxx Answered: tat X A 26308049 × 10 EKU-- SP 25: X E DNA Sequence x H. pylor vo/index.html?elSBN=9780357038406&id=339416021&snapshotld=877369& MINDTAP its, and the Derivative 44. Answer 5 X -10-5 5 10 -5. f(x) = 2 + x +5 if x 0 3 4 f(x) = x² - 1 x+1 if x = -1 MacBook Pro G Search or type URL if x = -1 + AA aarrow_forwardCalculus lll May I please have an explanation of the multivariable chain rule in the example given? Thank youarrow_forward
- Mind Tap - Cenxxx Answered: tat X A 26308049 X 10 EKU-- SP 25:1 x E DNA Sequence x H. pyl /nb/ui/evo/index.html?elSBN 9780357038406&id=339416021&snapshotid=877369& ⭑ SAGE MINDTAP a ons, Limits, and the Derivative 吃 AA In Exercises 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, and 56, find the values of x for which each function is continuous. 45. f(x) = 2x²+x-1 Answer▾ 46. f(x) = x³- 2x²+x-1 47. f(x) 2 = x²+1 Answer 48. f(x) = 49. f(x) = Answer 50. f(x) = 51. f(x) = I 2x²+1 2 2x - 1 x+1 x-1 2x + 1 x²+x-2 Answer↓ 52. f(x)= = x-1 x2+2x-3 53. $ % MacBook Proarrow_forward37. lim f (x) and lim f (x), where x+0+ x 0 Answer -> 38. lim f (x) and lim f (x), where +0x x―0M 2x if x 0arrow_forward37. lim f (x) and lim f (x), where x+0+ x 0 Answer -> 38. lim f (x) and lim f (x), where +0x x―0M 2x if x 0arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning





