is a polynomial function. The domain of any polynomial function is the set of all real numbers, making that the correct choice.

The domain of a square root function is the set of all values of for which the radicand is nonnegative. Three of these functions are undefined for at least one value of , since this value yields a negative radicand. 

 is outside the domain of , , and by virtue of causing their radicands to be negative:

:

We examine . We show that the radical can never be negative by setting it as such, and trying to solve for , as follows:

Since must be nonnegative, it is always greater than . Therefore, the inequality has no solution. Consequently, the radicand of is always nonnegative, and has the set of all real numbers as its domain.

This function resembles a parabola since the highest order is within the term .

There are no denominators where the  variable is undefined.  

The domain refers to the existing x-values which lie on the graph.

This parabola will only shift upward eight units and will not affect the domain.

The answer is:  

The easiest way to figure this out is by knowing that the domain of all quadratics without any restrictions is always all real numbers, though this problem can be solved graphically, too.

Either method is correct and your correct answer is:

It is important, too, to note that soft brackets must be used when working with infinity. 

There are two important components of this problem. First we must set the denominator equal to zero and solve for . This gives us values that  can't be because the denominator can never equal zero.

Doing this, we get , so,  can be any number except for a positive two.

The other key to this problem is knowing the difference between brackets and parentheses. The square brackets mean that a number is included, whereas the parentheses mean that it is not. Because  cannot equal 2, we need to use the parentheses.

This makes:

From the figure one can see the Range varies from  to .

The question states that the sequence is arithmetic, which means we find the next number in the sequence by adding (or subtracting) a constant term. We know two of the values, separated by one unknown value.

We know that  is equally far from -1 and from 13; therefore  is equal to half the distance between these two values. The distance between them can be found by adding the absolute values.

The constant in the sequence is 7. From there we can go forward or backward to find out that .

By taking the difference between two adjacent numbers in the sequence, we can see that the common difference increases by one each time.

Our next term will fit the equation , meaning that the next term must be .

After , the next term will be , meaning that the next term must be .

Finally, after , the next term will be , meaning that the next term must be

The question asks for the sum of the next three terms, so now we need to add them together.

First, find a pattern in the sequence.  You will notice that each time you move from one number to the very next one, it increases by 7.  That is, the difference between one number and the next is 7.  Therefore, we can add 7 to 36 and the result will be 43.  Thus .

The sequence follows the pattern for the equation:

Therefore,