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To discuss: the given rational function
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Answer to Problem 33RE
Explanation of Solution
Given:
Calculation:
STEP 1: The numerator and the denominator of
The domain of
Since 0 is in the domain, find the
Substitute 0 for
Therefore, the
STEP 2: The function
Determine the behaviour of the graph near the
Plot the point (-2,0) and indicate a line with slope -1 on the graph.
STEP 3: G is in lowest terms. The real zeros of the denominator are the real solutions of theequation
Graph the asymptote
STEP 4: Degree of the numerator is equal to the degree of the denominator. So, the graph has a horizontal asymptote. The leading coefficient of the numerator is 1 and that of the denominator is also 1 . Therefore, the graph of
Indicate this line on the graph using a dashed line.
Substitute
Multiply both the sides by
Subtract
There is no solution for
STEP 5: The zeros of the numerator and the denominator. - 1. - 2, and 2. Divide the x-axis into four intervals. The four intervals are
Now, construct the table.
Plot the points from the table obtained.
STEP6: Next, the behaviour of the graph near the asymptotes is to be determined.
The graph lies above the x -axis for x<-2 and y=1, is a horizontal asymptote. So, the graph is drawn at the top of the x -axis just approaching the asymptote $y=1$ at the bottom. Also note thatthe graph intersects the x-axis at the point (-2,0) .
The graph is drawn below the
The graph is drawn above the
The graph lies above the
STEP7: The figure shows the final graph.
Conclusion:
Thus, the given relation is discussed
Chapter 4 Solutions
Precalculus
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