(a)
To find:The domain of function.
(a)
Answer to Problem 52E
The domain of function is all the real numbers except
Explanation of Solution
Given information:
The function is
Calculation:
Consider the function.
.
The function is valid for all the real numbers except
Therefore, the domain of function is all the real numbers except
(b)
To find:The intercepts.
(b)
Answer to Problem 52E
The y- intercept is absent and the x- intercept is
Explanation of Solution
Given information:
The function is
Calculation:
The y intercept is absent as the function becomes undefined.
Equate function to zero to find x intercept.
Therefore, the y- intercept is absent and the x- intercept is
(c)
To find:The asymptotes.
(c)
Answer to Problem 52E
The slant asymptote is
Explanation of Solution
Given information:
The function is
Calculation:
In given function degree of numerator is one more than the degree of denominator. The graph will have slant asymptote which can be calculated by dividing numerator wuth denominator.
Here the slant asymptote will be
Therefore, the slant asymptote is
(d)
To find:The sketch of graph.
(d)
Answer to Problem 52E
The graph is shown in Figure-(1).
Explanation of Solution
Given information:
The function is
Calculation:
The below table shows additional points
Test Interval | Value of x | Value of f | Sign | Point of f |
-2 | Positive | |||
Negative | ||||
Positive | ||||
2 | Negative |
Draw the sketch for the function by using the equations of asymptotes.
Figure-(1)
Therefore, the graph is shown in Figure-(1).
Chapter 2 Solutions
EBK PRECALCULUS W/LIMITS
- 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