(a)
To find:The domain of function.
(a)
Answer to Problem 28E
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 of the equation.
(b)
Answer to Problem 28E
The y- intercept is
Explanation of Solution
Given information:
The function is
Calculation:
Put
The y- intercept is
Equate
The x- intercept is
Therefore, the y- intercept is
(c)
To find:The asymptotes of the function.
(c)
Answer to Problem 28E
The vertical asymptote is
Explanation of Solution
Given information:
The function is
Calculation:
Calculate vertical asymptote by finding solution of denominator.
The degree of numerator is same as the degree of denominator so the horizontal asymptote will be ratio of leading coefficient of numerator to denominator which is unity for numerator as well as denominator.
So horizontal asymptote is
Therefore, the vertical asymptote is
(d)
To find:The sketch of graph.
(d)
Answer to Problem 28E
The graph is shown in Figure-(1).
Explanation of Solution
Given information:
The function is
Calculation:
The additional points are tabulated below.
Test Interval | Value of x | Value of f | Sign | Point of f |
-4 | Positive | |||
-2.5 | -1.18 | Negative | ||
1 | Positive | |||
3.5 | Negative | |||
5 |
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