To graph: For the function that satisfies the given conditions.
The given conditions .
In the given conditions, the domain is divided into seven intervals: .
In the interval , the function is decreasing since and has positive curvature since .
Sketch a line for this part of the function.
Since , plot the point . Then the graph a line for the interval .
Since , increasing in this interval. Since , it has positive curvature.
In the interval , is increasing since and has negative curvature since . Sketch a line for this part of function.
In the interval , the function is decreasing and has negative curvature. In addition, is an asymptote because .
In the interval , the function is increasing and has negative curvature. It starts from and goes up.
In the interval , the function is decreasing because .
It has negative curvature because .
Finally, In the last interval , the function is decreasing and has positive curvature. In addition, the function approaches from above because .
Interpretation: Graph for the function is shown in figure (1).
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