SOLUTION: i need to analyze and graph f(x)= (x^3-1)/(x) please i need to finmd the domain of f, the range of f, the x-intercepts, the y-intercepts, the numbers at which f has a relative m

Question 109597: i need to analyze and graph f(x)= (x^3-1)/(x)
please i need to finmd the domain of f, the range of f, the x-intercepts, the y-intercepts, the numbers at which f has a relative maximum, the relative maxima of f, intervals at which f is increasing, and if f is even, odd or neither .....
i really need help :( thanks
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
i need to analyze and graph f(x)= (x^3-1)/(x)
please i need to
find the domain of f: All Real Numbers except x=0
-----------------
the range of f: all Real Numbers
-----------------
the x-intercepts; Let y = 0 and solve for x; x^3-1=0; x=cube rt (1) = 1
-------------------
the y-intercepts: Let x=0 and solve for y: y=-1/0; no y-intercepts
--------------------
the numbers at which f has a relative maximum
none
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The derivative = [x(3x^2)-(x^3-1)*1]/x^2
f'(x) = [3x^3-x^3+1]/x^2
Solve for x when f'(x)=0:
2x^3+1=0
x^3 = -1/2
x = (-1/2)^(1/3)= -0.7937...
------------
the relative maxima of f
No relative maximum
--------------------
intervals at which f is increasing
(-0.7937..,0) U (0,+inf)
----------------------
and if f is even, odd or neither .....
f(x) does not equal f(-x) so f is not even
f(-x) does not equal -f(x) so f is not odd
f is neither odd nor even
-------------------------------------
Graph:

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Cheers,
Stan H.

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