# determine all axis intercepts and asymptotes

• Apr 8th 2009, 06:40 AM
oneway1225
determine all axis intercepts and asymptotes
how do you find the axis intercepts and asymptotes

f(x)=(3x^2-2x)/(x^2-4)
• Apr 8th 2009, 07:54 AM
skeeter
Quote:

Originally Posted by oneway1225
how do you find the axis intercepts and asymptotes

f(x)=(3x^2-2x)/(x^2-4)

$f(x) = \frac{x(3x-2)}{(x+2)(x-2)}$

$f(0) = 0$ ... y-intercept

$f(x) = 0$ at $x = 0$ and at x = \frac{2}{3} ... x-intercepts

vertical asymptote, $x = -2$ and x = 2 ... $(x+2)(x-2)$ in the denominator

horizontal asymptote at $y = 3$ ... degree of the numerator = degree of the denominator ... ratio of the leading coefficients in the numerator and denominator gives you the value of the horizontal asymptote.
• Apr 8th 2009, 08:00 AM
Prove It
Quote:

Originally Posted by oneway1225
how do you find the axis intercepts and asymptotes

f(x)=(3x^2-2x)/(x^2-4)

First note that $x \neq \pm 2$

X intercept:

$0 = \frac{3x^2 - 2x}{x^2 - 4}$

$0 = 3x^2 - 2x$

$0 = x(3x - 2)$

$x = \left\{0, \frac{2}{3}\right\}$.

Y intercept:

$y = \frac{3(0)^2 - 2(0)}{0^2 - 4}$

$y = \frac{0}{-4}$

$y = 0$.

Asymptotes:

$x = \pm 2$
• Apr 8th 2009, 08:01 AM
masters
Quote:

Originally Posted by skeeter
$f(x) = \frac{3x(x-2)}{(x+2)(x-2)}$

$f(0) = 0$ ... y-intercept

$f(x) = 0$ at $x = 0$ ... x-intercept

vertical asymptote, $x = -2$ ... $(x+2)$ in the denominator

removable discontinuity (a "hole") at $x = 2$ ... $(x-2)$ in both numerator and denominator

horizontal asymptote at $y = 3$ ... degree of the numerator = degree of the denominator ... ratio of the leading coefficients in the numerator and denominator gives you the value of the horizontal asymptote.

The numerator is $3x^2-2x$ or $x(3x-2)$, not $3x^2-6x$, so we have 2 vertical asymptotes and no hole. The other vertical asymptote is at $x=2$
• Apr 8th 2009, 08:04 AM
stapel
Quote:

Originally Posted by oneway1225
how do you find the axis intercepts and asymptotes

To learn the general rules, study some online lessons on asymptotes and intercepts. Then please return here and review the solutions you were provided for this particular exercise, and confirm that you understand the concepts and methods they used.

(Wink)