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 polynomial has a domain as all the real numbers except for 4.
The provide function can be rewritten as:
The function will return all possible values less than and all values above 6. 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 y-intercept is and there is no x-intercept.
The function has a vertical asymptotes as the denominator is not defined at those points.
The function can be rewritten as:
This implies that the line is the slant asymptote of the provided function.
Now, differentiate the function with respect to x and equate it to zero to obtain the critical points.
This gives four test intervals .
The function is increasing in this interval.
The function is decreasing in this interval.
The function is decreasing in this interval
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