Graphing Rational Functions with Vertical Asymptotes

[Glissando]

Homework Statement

Sketch the graphs of f(x) = (x^3)/(x^2-1) showing vertical and horizontal asymptotes and relative extrema

Homework Equations

Zeroes, limits

The Attempt at a Solution

I've actually figured out the question; No horizontal asymptote, max at (-sqrt(3), -3sqrt(3)/2), Dec. plateau at (0,0) and minimum at (sqrt(3), 3sqrt(3)/2) the only problem I have is with the vertical asymptote.

Vertical asymptote = + or - 1
Everything is fine until i get to:

lim -1³/(-1^-)²-1 = -1/0^- = +infinity
x->-1^-

But on my graphing calculator it shows it going towards negative infinity when it approaches -1 from the left side ):

Thanks for the help!

 

[Mark44]

Homework Statement

Sketch the graphs of f(x) = (x^3)/(x^2-1) showing vertical and horizontal asymptotes and relative extrema

Homework Equations

Zeroes, limits

The Attempt at a Solution

I've actually figured out the question; No horizontal asymptote, max at (-sqrt(3), -3sqrt(3)/2), Dec. plateau at (0,0) and minimum at (sqrt(3), 3sqrt(3)/2) the only problem I have is with the vertical asymptote.

Vertical asymptote = + or - 1
Everything is fine until i get to:

lim -1³/(-1^-)²-1 = -1/0^- = +infinity
x->-1^-

The limit is actually negative infinity. As you already know, the numerator approaches -1, but the denominator is close to zero and positive. Since x < -1, x² > 1, so x² - 1 > 0.

But on my graphing calculator it shows it going towards negative infinity when it approaches -1 from the left side ):

Thanks for the help!

 

[Glissando]

WOW that was like BAAAAAAAAAM. Thanks fo much (: