1. ## asymtote

i need to draw a graph of

x^2 + 1 / x

this is a asymtote type problem

can anyone help

thanks

2. Originally Posted by thrusterkel
i need to draw a graph of

x^2 + 1 / x

this is a asymtote type problem

can anyone help

thanks
Vertical asymptotes are where functions are undefined. Where is this function undefined at?

BTW, the best way to graph such problems is to graph each term seperately and then "add" the graphs.

3. Find the asymptote, find the limits when the function approaches -∞ and +∞, find a few points, find whether the function is symmetrical about x-axis or y-axis or the origin... and plot it.

4. i have made x = 0 so get the points 0,0 and made y = 0 but get a imaginary number is this right

5. Firstly, is it $\displaystyle \frac{x^2+1}{x}$ or $\displaystyle x^2 + \frac{1}{x}$ ?

6. $\displaystyle \frac{x^2+1}{x}$

7. Originally Posted by thrusterkel
$\displaystyle \frac{x^2+1}{x}$
In that case, graph it as $\displaystyle x+\frac{1}{x}$

For $\displaystyle x>1$, it follows the path slightly above $\displaystyle f(x)=x$.

Likewise, for $\displaystyle x<1$, it follows the path slightly under $\displaystyle f(x)=x$.

When $\displaystyle -1 \le x < 0$, the graph shoots down to negative infinity as it gets closer to zero.

When $\displaystyle 0 < x \le 1$, the graph shoots up to positive infinity as it gets closer to zero.