Analyzing the Graph of a Function In Exercises 5-34, analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results.
To graph: The function .
Given: The function .
Consider the provided function.
The function being a rational function has a domain as all the real numbers except 0.
The function will only return values that are greater than 1. This implies that the range of the function is .
Now find the x and y intercepts by equating and x to zero respectively to obtain:
There are no y-intercepts or x-intercepts.
The function has one vertical asymptote as the denominator is not defined at those points.
Hence, the horizontal asymptote is .
Now, differentiate the function with respect to x and equate it to zero to obtain the critical points.
This can never be zero and thus the function has no critical points.
This gives two test intervals .
The function is increasing in this interval
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