Sketch the graph of f(x) = (x^3) / x^3+1, using curve sketching.

[KJL]

Could someone please walk through the steps of curve sketching as i'm having difficulties with this question and i can't seem to get it figured out!
The questions is: Please Sketch the graph off(x) = (x^3) / x^3+1, using curve sketching.

 

[stapel]

Could someone please walk through the steps of curve sketching as i'm having difficulties with this question and i can't seem to get it figured out!

There are already loads of worked examples in your book and in your class notes (plus what you've studied from online), so one more worked example isn't likely to make a difference. Instead, please reply showing your work and thoughts.

Sketch the graph of f(x) = (x^3) / x^3+1, using curve sketching.

Would it be correct to assume that grouping symbols are missing, and that the function is actually "f(x) = (x^3)/(x^3 + 1)", which formats as follows?

. . . . .\(\displaystyle f(x)\, =\, \dfrac{x^3}{x^3\, +\, 1}\)

What steps does your particular textbook require for doing graphs? You know the stuff from algebra: x- and y-intercepts, horizontal and vertical asymptotes, a T-chart with some values, etc. From calculus, you know about the First and Second Derivative Tests. And so forth.

Where are you stuck? Please be specific. Thank you!