The function is .

Find the intercept :

To find the -intercept, substitute in the function.

The-intercept is 

To find the -intercept, substitute in the function.

The -intercept is .

Find the relative extrema for the function :

Consider .

Differentiate on each side  with respect to .

Quotient rule of derivatives : .

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Find the critical numbers by equating to .

.

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Imaginary roots are not considered.

There is no critical points.

Therefore, there is no relative extremum points and the function is decreasing for all values of .

Find the points of inflection :

The first derivative of is .

Differentiate on each side with respect to .

.

Quotient rule of derivatives : .

.

The second derivative of is .

To find inflection points we make.

.

,

, .

, and .

Imaginary roots are not considered.

The inflection point occurs at .

If , then .

Thus, the inflection point is .

Find the asymptotes :

Vertical asymptote :

The function is .

Vertical asymptote exist when denominator is zero.

Equate denominator to zero.

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Thus, the vertical asymptotes are and .

Horizontal asymptote :

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

Thus, the horizontal asymptote is .

Graph :

Draw a coordiante plane.

Graph the function .

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Note : The dashed lines indicates horizontal and vertical asymptotes.

Intercept : .

Relative extremum points : none.

Inflection point : .

Vertical asymptotes : and .

Horizontal asymptote : .

Graph of the function :

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