Concept explainers
a.
To check whether the function is identical or not.by including the graphs, the asymptotes, intercepts and the domain.
The functions are identical.
Given:
The given functions are:
Concept Used:
For y - intercept put x =0 and for x -intercept put y =0.
Vertical asymptotes occur at the values where a rational function has a denominator of 0
Horizontal asymptote is of the form y = k where x→8 or x→ -8
Calculation:
The graph of both the functions
using online calculator is as shown below:
As the graph of both the function is same
The x intercept is x =-2 and the y -intercept is y =2.
There is no vertical asymptote and no horizontal asymptote.
The domain of the function f(x) is all real values except 1.The domain of the function g(x) is all real values.
Conclusion:
The functions are identical.
b.
To check whether the function is identical or not.by including the graphs, the asymptotes, intercepts and the domain.
The functions are identical.
Given:
The given functions are:
Concept Used:
For y - intercept put x =0 and for x -intercept put y =0.
Vertical asymptotes occur at the values where a rational function has a denominator of 0
Horizontal asymptote is of the form y = k where x→8 or x→ -8
Calculation:
The graph of both the functions
using online calculator is as shown below:
As the graph of both the function is same
The x intercept is
The functions have no vertical asymptote and no horizontal asymptote.
The domain of the function f(x) is all real values except -1. The domain of the function g(x) is all real values.
Conclusion:
The functions are identical.
c.
To check whether the function is identical or not.by including the graphs, the asymptotes, intercepts and the domain.
The functions are identical.
Given:
The given functions are:
Concept Used:
For y - intercept put x =0 and for x -intercept put y =0.
Vertical asymptotes occur at the values where a rational function has a denominator of 0
Horizontal asymptote is of the form y = k where x→8 or x→ -8
Calculation:
The graph of both the functions
using online calculator is as shown below:
As the graph of both the function is same
There is no x intercept and the y -intercept is y =-1.
The vertical asymptote is x =1 and horizontal asymptote.is y =0
The domain of the function f(x) is all real values except -1and 1. The domain of the function g(x) is all real values except x=1
Conclusion:
The functions are identical.
Chapter 2 Solutions
Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition
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