We can only have an oblique asymptote if the degree of the numerator is one more than the degree of the denominator.  This stipulates that  must equal .  

The slope of the asymptote is determined by the ratio of the leading terms, which means the ratio of  to  must be 3 to 1.  The actual numbers are not important.

Finally, since the value of  is at least three, we know there is no intercept to our oblique asymptote.

To find the y-intercept of , simply substitute  and solve for .

The y-intercept is 1.

The numerator, , can be simplified by factoring it into two binomials.

There is a removable discontinuity at , but there are no asymptotes at  since the  terms can be canceled.

The correct answer is:  

The -intercept(s) is/are the root(s) of the numerator of the rational functions.

In this case, the numerator is .

Using the quadratic formula,

the roots are .

Thus,  are the -intercepts.

Finding the vertical asymptotes of the rational function  amounts to finding the roots of the denominator, .

It is easy to check, using the quadratic formula,

that the roots, and thus the asymptotes, are .

Before we start to simplify the problem, it is crucial to immediately identify the domain of this function .

The denominator cannot be zero, since it is undefined to divide numbers by this value.  After simplification, the equation is:

The domain is  and there is a hole at  since there is a removable discontinuity.  There are no asymptotes.  

Since it's not possible to substitute  into the original equation, the y-intercept also does not exist.

Therefore, the correct answer is:

To find the vertical asymptote of a function, we set the denominator equal to . 

With our function, we complete this process. 

The denominator is , so we begin: 

The y-intercept of a function is always found by substituting in .

We can go through this process for our function. 

In order for the vertical asymptote to be , we need the denominator to be . This gives us three choices of numerators:

If the slant asymptote is , we will be able to divide our numerator by and get with a remainder.

Dividing the first one gives us with no remainder.

Dividing the last one gives us with a remainder.

The middle numerator would give us what we were after, with a remainder of -17.

The answer is

To find the information we're looking for, we should factor this equation:

This means that it simplifies to .

When the equation is in the form of a fraction, to find the zero of the function we need to set the numerator equal to zero and solve for the variable.

To find the asymptote of an equation with a fraction we need to set the denominator of the fraction equal to zero and solve for the variable.

Therefore our equation has a zero at -3 and an asymptote at -2.

To find the vertical asymptote, just set the denominator equal to 0:

To find the slant asymptote, divide the numerator by the denominator, but ignore any remainder. You can use long division or synthetic division.

The slant asymptote is

.