The function is .

Domain :

The function .

Denominator of the should not be and function under the squareroot cannot be negative.

Thus, the domain of the function  is .

Intercepts :

- intercept :

To find the - intercept, substitute  in the function.

There is no - intercept.

 - intercept :

To find the - intercept, substitute  in the function.

 is not in the domain of the function, hence it is not considered.

Thus, there is no  - intercept.

Symmetry :

If , then the function  is even and it is symmetric about -axis.

If , then the function  is odd and it is symmetric about origin.

Here .

The function  is odd.

Thus, the function  is symmetric about origin.

Vertical Asymptote :

Vertical asymptote exists where denominator is zero.

Equate denominator to zero.

Vertical asymptote is .

Horizontal asymptote:

The line  is called a horizontal asymptote of the curve  if either  or 

Thus, the horizontal asymptote is .

Intervals of increase or decrease :

Differentiate on each side  with respect to :

.

 is never zero on its domain. 

\ Interval \	Test Value	Sign of	Conclusion
		\ \	decreasing
		\ \	\ decreasing \

is decreasing on its domain because .

Determination of extrema :

 is an decreasing function, hence there is no chance of local minimum or maximum.

Determination of inflection point:

.

Differentiate on each side  with respect to :

.

 is never zero.

Hence, there is no inflection points.

But at  the function is undefined.

Consider the test intervals as  and .

\ Interval \	Test Value	Sign of	Concavity
		\ \	Up
		\ \	\ Down \

Thus, the graph is concave up on the interval .

The graph is concave down on the interval .

Graph of the function :

Graph of the function  is 

.