For the function , it is not necessary to graph the function.  The y-intercept does not affect the location of the asymptotes.

Recall that the parent function  has an asymptote at  for every  period.  

Set the inner quantity of  equal to zero to determine the shift of the asymptote.

This indicates that there is a zero at , and the tangent graph has shifted  units to the right.  As a result, the asymptotes must all shift  units to the right as well.  The period of the tangent graph is .

Factor the numerator and denominator.

Notice that the  terms will cancel.  The hole will be located at  because this is a removable discontinuity.

The denominator cannot be equal to zero.  Set the denominator to find the location where the x-variable cannot exist.

The asymptote is located at .

To find the vertical asymptotes, we set the denominator of the function equal to zero and solve.

We know that the parent function  has vertical asymptotes at  where  is any integer. We will set the quantity inside the  function equal to zero to solve for the shift of the asymptote.

Now we must add this to the asymptotes of the parent function:

We know that the parent function  has asymptotes at  where  is any integer.  We will set the quantity within the  function equal to zero in order to find the shift of the asymptote. 

Now we must add this to the asymptotes of the parent function:

 If you do not have these asymptotes memorized, they can be easily derived.  Write  in terms of .

Now we need to solve for  since it is the denominator of the function.  When the denominator of a function is equal to zero, there is a vertical asymptote because that function is then undefined. 

 when .  So for any integer , we say that there is a vertical asymptote for  when .

We know that the parent function  has vertical asymptotes at .  So now we will set the inner quantity of the  function equal to zero to find the shift of the asymptote.

Now we will add this to the parent function equation for vertical asymptotes

Now we will set this equation for the given vertical asymptote at

We know that the parent function of  has asymptotes at  where  is any integer.  Considering  we can set the asymptotic equation equal to this one and solve for  to see if  is an integer.  If  is an integer, then there is a vertical asymptote here.

So when , then

, so the given statement is true.

Do not confuse the movement of an equation of a line with the movement of a point.  Moving  two units to the right has no effect on the equation of the horizontal line.  Moving the equation two units down will change the horizontal line equation to .

Which of the following expressions corresponds to a  vertical translation of f(x) 

In my experience, vertical translations are the easiest way of changing a graph. A vertical translation will be of the form:

What this basically means is that we simply add our vertical translation onto the end of our function. This will simply make our function +c higher. In this case we need a vertical translation of positive 5. Do the following:

So our answer is: