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To discuss: the given rational function.
![Check Mark](/static/check-mark.png)
Answer to Problem 25RE
Explanation of Solution
Given:
Explanations:
Step
The numerator and the denominator is in the factored form.
Find the domain of the function.
The domain of
Therefore, there is no
Step
The function
Determine the behavior of the graph near the
Plot the point
Step
By the zero-Product Property, solve the equation and get
Graph these asymptotes using a dashes line.
Step
Degree of the numerator is less than the degree of the denominator. So,
So, the line
Indicate this line on the graph using a dashed line.
Substitute
Multiply by
Subtract
The only solution is
Step
The zero of the numerator is
The four intervals are
Now, construct the table.
Interval | ||||
Number chosen | ||||
Value of | ||||
Location of graph | Below | Above | Below | Above |
Point on graph |
Plot the points from the table obtained.
Step
Next, the behavior of the graph near the asymptotes is to be determined.
The line
The vertical asymptote is the line
The graph is below
Also, the graph is below the
The line
The line
Step
The figure shows the final graph.
Conclusion:
Therefore,the given rational function is analyzed.
Chapter 4 Solutions
Precalculus
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