1. ## Intercepts and Aysmptotes

I have got a confusing question that does not lead me to any solution. I also got a sketch a graph but unfortunately I dont have a graphical calculator. The question is given below. All help would be welcomed! This question is really confusing me..... Pls help.....

The question is :

Draw a careful sketch, showing and labeling all intercepts and asymptotes of
y = x^3 + 2x^2- x - 2 / x^2 + x - 6

2. Originally Posted by vikas3296
I have got a confusing question that does not lead me to any solution. I also got a sketch a graph but unfortunately I dont have a graphical calculator. The question is given below. All help would be welcomed! This question is really confusing me..... Pls help.....

The question is :

Draw a careful sketch, showing and labeling all intercepts and asymptotes of
y = x^3 + 2x^2- x - 2 / x^2 + x - 6
$\displaystyle y = \frac{x^3+2x^2-x-2}{x^2+x-6}$

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

$\displaystyle y = \frac{(x+2)(x^2-1)}{(x+3)(x-2)}$

$\displaystyle y = \frac{(x+2)(x+1)(x-1)}{(x+3)(x-2)}$

x-intercepts ... $\displaystyle x = -2$ , $\displaystyle x = -1$ , $\displaystyle x = 1$

y-intercept ... $\displaystyle y = \frac{1}{3}$

vertical asymptotes ...$\displaystyle x = -3$ , $\displaystyle x = 2$

slant asymptote ... perform long division on the original expression to find it.