Please, I need the answers of other tutors to check, thank you very much! Find the vertical and horizontal asymptotes of f(x), find the first and second derivatives and draw the graph of the following function.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 35E
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Please, I need the answers of other tutors to check, thank you very much!

Find the vertical and horizontal asymptotes of f(x), find the
first and second derivatives and draw the graph of the following function. Be precise on the values in the range -4 to 4 and on the critical values of the derivatives:

f(x)= ( (x^3)+8) / ((x^3-8))
 
         How would the graph change if it were f(x) =   ( (x^3)+8) / ((x^3-8)) +1
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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,