The vertical asymptote(s) of the graph of a rational function such as  can be found by evaluating the zeroes of the denominator after the rational expression is reduced. The expression is in simplest form, so set the denominator equal to 0 and solve for :

The graph of the line  is the only vertical asymptote of the graph of .

The vertical asymptote(s) of the graph of a rational function such as  can be found by evaluating the zeroes of the denominator.

Set the denominator equal to 0 and solve for :

The only vertical asymptote of the graph is the line of the equation .

The -intercept of the graph of a function is the point at which it intersects the -axis. The -coordinate is 0, so the -coordinate can be found by evaluating . This is done by substitution, as follows:

The value of the denominator here is 0, so  is an undefined quantity. Consequently, the graph of  has no -intercept.

The vertical asymptote(s) of the graph of a rational function such as  can be found by evaluating the zeroes of the denominator after the rational expression is reduced. 

First, factor the numerator and denominator.

The numerator is a perfect square trinomial and can be factored as such:

The denominator can be factored as the difference of squares:

Rewrite

as

The expression can be reduced by cancelling  in both halves:

Set the denominator equal to 0 and solve:

The only vertical asymptote is therefore the line of the equation .

The vertical asymptote(s) of the graph of a rational function such as  can be found by evaluating the zeroes of the denominator after the rational expression is reduced. 

First, factor the numerator. It is a quadratic trinomial with lead term , so look to "reverse-FOIL" it as

We seek two integers whose sum is  and whose product is ; through trial and error, we find  and 2, so

Therefore,  can be rewritten as 

Cancelling , this can be seen to be essentially a polynomial function:

which does not have a vertical asymptote.

The -intercept(s) of the graph of  are the point(s) at which it intersects the -axis. The -coordinate of each is 0; their -coordinate(s) are those value(s) of  for which , so set up, and solve for , the equation:

A fraction is equal to 0 if and only if the numerator is equal to 0, so set 

Factor out :

By the Zero Product Property, one of the factors must be equal to 0, so either

or 

in which case

. 

However, setting  in the definition, we see that

, an undefined expression due to the zero denominator. 5 cannot be eliminated similarly. Therefore,  is the only -intercept.

The inverse function  of a function  can be found as follows:

Replace  with :

Switch the positions of  and :

or

Solve for . This can be done as follows:

Square both sides:

Add 9 to both sides:

Multiply both sides by , distributing on the right:

Replace  with :

The statement is false. Look for the point on the graph of  with -coordinate  by going right  unit, then moving up and noting the -value, as follows:

, so the statement is false.

The -intercept of the graph of a function is the point at which it intersects the -axis (the vertical axis). That point is marked on the diagram below:

The point is about one and three-fourths units above the origin, making the coordinates of the -intercept .

This is the composition of two functions. By definition, .  To find the range of , we need to find the values of this function for each value in the domain of . Since , this is equivalent to evaluating  for each value in the range of , as follows:

Range value: 3 

Range value: 5

Range value: 8

Range value: 13

Range value: 21

The range of  on the set of range values of  - and consequently, the range of  - is the set . Of  the five choices, only 45 does not appear in this set; this is the correct choice.