The domain is the set of possible value for the variable. We can find the impossible values of by setting the denominator of the fractional function equal to zero, as this would yield an impossible equation.

Now we can solve for .

There is no real value of that will fit this equation; any real value squared will be a positive number.

The radicand is always positive, and is defined for all real values of . This makes the domain of the set of all real numbers.

In determining the domain of a function, we must ask ourselves where the function is undefined. To do this for our function, we must set the denominator equal to zero, and solve for x; at this x value, we get a zero in the denominator of the function which produces an undefined value.

This is the only limitation for the domain of the function, so our domain is

The domain consists of all values that the input can be without making the output unreasonable. In our problem, the only condition that would dissatisfy the equations parameters is a negative inside the square root. However, having inside the square root makes this a bit tricky, because we have to consider that squaring this value will always yield something positive. Thus, we cannot have any values of whose squares are strictly less than . Thus, the domain must be all values of that are greater than or equal to and less than or equal to .

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:

To solve this equation you must look at the denominator since the denominator can never equal zero.

You need to set the denominator equal to then solve for .

, then square root both sides to get

, the value that cannot be, therefore, is .

A relation is a function if and only if no -coordinate is paired with more than one -coordinate. We test each of these four values of to see if this happens.

:

The points become:

Since -coordinate 1 is paired with two -coordinates, 2 and 9, the relation is not a function.

:

The points become:

Since -coordinate 3 is paired with two -coordinates, 0 and 9, the relation is not a function.

:

The points become:

Since -coordinates 3 and 5 are each paired with two different -coordinates, the relation is not a function.

:

The points become:

Since each -coordinate is paired with one and only one -coordinate, the relation is a function. is the correct choice.

The terms inside a square root cannot be negative, but can be equal to zero.

Set the terms inside the square root to zero to determine where the domain will begin.

The value of cannot be less than negative two, but can be more than negative two. The negative sign in front of the square root symbol will flip the graph across the x-axis, and will not affect the domain.

The domain is:

The value of the inner term of a square root cannot be negative. This means that no number can be less than zero.

Set the inner term equal to zero and solve for .

This means that cannot be less than this value.

Therefore, the exists for every number equal to or greater.

The answer is:

At , there is a hole in this function:

At all other values of x, both positive and negative, this function will be defined.

The domain is the set of x-values that make the function defined.

This function is defined everywhere except at , since division by zero is undefined.