Remember , for .

Step 1, realize where starts: A) observe never occurs, B) zero-out the radical component of ;

C) The resulting point is .

Step 2, find simple points for after :

, so use ;

The next resulting point; .

, so use ;

The next resulting point; .

Step 3, draw a curve through the considered points.

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.

Factor:

Double check by factoring:

Add together:

Therefore:

To solve this, first, find the common denominator. It is (n+1)(n-2). Multiply the entire equation by this:

Simplify to get:

Expand to get:

Move all terms to one side and combine to get:

Use the quadratic formula to get:

Use the grouping method to factorize common terms:

This one is a bit of a journey. The expressions for the first two zeroes are easily calculated, and respectively. The last expression must be broken up into two equations: which are then set equal to zero to yield the expressions and

Finally, we multiply together all of the parenthesized expressions, which multiplies out to

First, we need to get this function into a more standard form.

Now we can see that while the function is being horizontally compressed by a factor of 2, it's being translated 3 units to the right, not 6. (It's also being vertically stretched by a factor of 4, of course.)

First, we need to get this function into a more standard form.

Now we can see that while the function is being horizontally compressed by a factor of 2, it's being translated 3 units to the right, not 6. (It's also being vertically stretched by a factor of 4, of course.)

We can accomplish this division by re-writing the problem as a fraction.

The denominator will distribute, allowing us to address each element separately.

Now we can cancel common factors to find our answer.

Starting with

moves the parabola by units to the right.

Similarly moves the parabola by units to the left.

Hence the correct answer is option .