can anyone help me in graphing this ?
f(x) = whole sqrt x + 3/x - 2
$\displaystyle y = \sqrt{\frac{x+3}{x-2}} = \sqrt{\frac{[x-2]+5}{x-2}} = \sqrt{1 + \frac{5}{x-2}}$.
First of all you should establish the implied domain. You need $\displaystyle x + 3 \geq 0$ AND x - 2 > 0 => ......, OR $\displaystyle x + 3 \leq 0$ AND x - 2 < 0 => ......
There's no y-intercept (why?).
x-int: Solve x + 3 = 0 (why?).
Vertical asymptote is got from solving x - 2 = 0 (why?).
Horizontal asymptote: As $\displaystyle x \rightarrow \pm \infty$, y --> 1 (why?). In fact, as x --> -oo, y --> 1 from below (why?) and as x --> +oo, y --> 1 from above (why?)
Stationary points: Solve dy/dx = 0. (Hint: There are none).
Now draw the shape that ties all these features together .....