To find the range, we first need to find the domain of the function. Then we will determine the range by finding the output values based on the domain.

First, we can factor out x from the denominator:

Since the function will be undefined when the denominator equals 0, we know that x=0 and x=1 are not in the domain of this function. We also know that this function is undefined for all negative number since the function includes a root of an even degree. The exponent under the square root does not change this, since cubing a negative number will still result in a negative number, as with any odd degreed exponent. 

So, this function is defined at all non-negative values except for 0 and 1.

The domain is defined as the input values or x values of a set.

So domain: 4,3,7

The range is defined as the output values or y values of a set.

So range: 2,7,3

In order for the set to be a function, each input value must have only one corresponding output value. In this example, the input value 4 has two output values: 2 and 3. The set is not a function.

The domain of a set of ordered pairs is the  values.

The  values are the first number in each set of coordinates.

The  values are:

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 .

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 .

The domain is defined as the input values or x values of a set. We can see that x is never less than zero

So domain: 0 ≤ x < ∞

The range is defined as the output values or y values of a set. We can see that we reach all values of y

So range: y = all real numbers

In order for the set to be a function, each input value must have only one corresponding output value. Another way of interpreting this graphically is that the graph must be able to pass the vertical line test. If we draw a vertical line on this graph, it corsses the parabola twice. This means there are multiple y output values for a single x input value.

Therefore, the graph is not a function

Begin by factoring the denominator to get: 

.

Do not simplify further! Realize that any value of "x" that causes the denominator to equal zero is not included in the domain of the function.

Therefore, one can see that the domain does not include x values of 8 or -2. No other gaps exist in this function so one can definitively say the domain is characterized by .

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:  

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:  

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