# How do you graph #f(x)=(x^3-2x^2-3x)/(4x^2+8x)# using holes, vertical and horizontal asymptotes, x and y intercepts?

##### 1 Answer

Factor then analyze!

#### Explanation:

We can factor both the top and the bottom to get asymptotes, some intercepts, and holes.

We see that they both have a zero in common (x=0), which means that

Since the bottom also goes to zero at

Last thing we need to observe: the top and bottom are different orders. Since the top is a higher order, in the limit, the equation will look like

Now we have everything except exact signs.

At

It then goes toward negative infinity and jumps to positive infinity after -2, until the next zero, i.e.

At x=-1, it hits zero and switches sign, i.e.

After x=3, the sign doesn't switch and the function quickly approaches that line, i.e.

From all of that analysis, you should be able to sketch a plot similar to this: graph{x(x-3)(x+1)/(4x(x+2)) [-13.86, 13.86, -6.93, 6.93]}