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

The contents inside the square root cannot be less than zero.

Set the inner quantity equal to zero. 

Find .  This is the critical point.  Add  on both sides and then divide by two on both sides.

We will test numbers less than and more three halves.

Let:  

Let:  

The negative inside the square square root indicates that this is an imaginary term.

This tells us that the domain is satisfied when  is less than or equal to .

The correct answer is:  

The domain of a rational function is the set of all real numbers except for the value(s) of that make the denominator zero. The value(s) can be found as follows:

The domain is the set of all real numbers except - or .

Since the radicand of a square root must be nonnegative, the domain of a radical function with a square root can be found by setting the radicand greater than or equal to 0:

This is the domain, which can also be stated as .

Since the radicand of a square root must be nonnegative, the domain of a radical function with a square root can be found by setting the radicand greater than or equal to 0:

[note the switch of symbol because of division by a negative number]

This is the domain, which can also be stated as .

The domain of a rational function is the set of all real numbers except for the value(s) of that make the denominator zero. The value(s) can be found as follows:

However, there is no real value of whose square is , so this statement has no solution. Therefore, there is no real value of which makes the denominator zero. The domain of is consequently the set of all real numbers.