how do you find the axis intercepts and asymptotes

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

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- Apr 8th 2009, 05:40 AMoneway1225determine 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, 06:54 AMskeeter

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

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

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

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

horizontal asymptote at $\displaystyle y = 3$ ... 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, 07:00 AMProve It
First note that $\displaystyle x \neq \pm 2$

X intercept:

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

$\displaystyle 0 = 3x^2 - 2x$

$\displaystyle 0 = x(3x - 2)$

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

Y intercept:

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

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

$\displaystyle y = 0$.

Asymptotes:

$\displaystyle x = \pm 2$ - Apr 8th 2009, 07:01 AMmasters
- Apr 8th 2009, 07:04 AMstapel
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)