The domain of any polynomial function, such as , is the set of real numbers, as a polynomial can be evaluated for any real value of .

There is no restriction on the value of , as a cube root can be taken of any real number, regardless of sign. Since  is not restricted in value, neither is , and the domain of  is the set of real numbers.

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

However, there is no real number  for which this equation holds, as the square of any such number must be positive. Therefore, the domain of  does not exclude any real values, and the domain is the set of all real numbers.

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:

However,  does not have a real value. Therefore, the graph of  has no -intercept.

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:

For this quantity to be equal to 0, it must hold that the numerator is equal to 0, so

This, however, is identically false, so  cannot be equal to 0 for any value of . It follows that the graph of  has no -intercept.

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:

For this quantity to be equal to 0, it must hold that the numerator is equal to 0, so

in which case

,

the correct choice.

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:

For this quantity to be equal to 0, it must hold that the numerator is equal to 0, so 

and

,

the correct choice.

The function  is defined for those values of  for which the radicand is nonnegative - that is, for which 

Subtract 25 from both sides:

Since the square root of a real number is always nonnegative, 

for all real numbers . Since the radicand is always positive, this makes the domain of  the set of all real numbers.

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 denominator. It is a quadratic trinomial with lead term , so look to "reverse-FOIL" it as

by finding two integers with sum 6 and product 5. By trial and error, these integers can be found to be 1 and 5, so 

Therefore,  can be rewritten as 

Set the denominator equal to 0 and solve for :

By the Zero Factor Principle,

or

Therefore, the binomial factor  can be cancelled, and the function can be rewritten as

If , then , so the denominator has only this one zero, and the only vertical asymptote is the line of the equation .