The -intercept of the graph of  is the point at which it intersects the -axis. Its -coordinate is 0; its -coordinate is , which can be found by substituting 0 for  in the definition:

,

the correct choice.

 is a rational function whose denominator polynomial has degree greater than that of its numerator polynomial (2 and 1, respectively). The graph of such a function has as its horizontal asymptote the line of the equation .

The -intercept of the graph of  is the point at which it intersects the -axis. Its -coordinate is 0; its -coordinate is , which can be found by substituting 0 for  in the definition:

An expression with 0 in the denominator is undefined, so 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. It is a quadratic trinomial with lead term , so look to factor 

by using the grouping technique. We try finding two integers whose sum is  and whose product is ; with some trial and error we find that these are  and , so, breaking the linear term:

Regroup:

Factor the GCF twice:

Therefore,  can be rewritten as 

Cancelling  in both halves of the equation:

Set the denominator equal to 0 and solve for :

The graph of  therefore has one vertical asymptotes - the line of the equation .

As a rational function,  has as its domain the set of all values for which the denominator is not equal to 0. Solve the equation

First, factor the quadratic trinomial as 

by finding two integers with sum  and product 25. From trial and error, we find the integers 5 and 5, so the equation can be rewritten as 

,

or

By the Square Root Property,

and 

.

Therefore, the only value excluded from the domain of  is , making the domain .

The -intercept of the graph of  is the point at which it intersects the -axis. Its -coordinate is 0; its -coordinate is , which can be found by substituting 0 for  in the definition:

,

the correct response.

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:

Add  to both sides:

Multiply both sides by 2:

,

the correct choice.

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 factor 

by using the grouping technique. We try finding two integers whose sum is  and whose product is ; with some trial and error we find that these are  and , so:

Break the linear term:

Regroup:

Factor the GCF twice:

Therefore,  can be rewritten as 

Cancel the common factor  from both halves; the function can be rewritten as

Set the denominator equal to 0 and solve for :

The graph of  therefore has one vertical asymptotes, the line of the equations . The line of the equation  is not a vertical  asymptote.

The -intercept of the graph of  is the point at which it intersects the -axis. Its -coordinate is 0; its -coordinate is , which can be found by substituting 0 for  in the definition:

,

the correct choice.