Let the function is .

Testing for symmetry.

x - axis : Replace y with - y.

Result is not a equivalent equation, so symmetric with respect x - axis is failed.

y - axis : Replace x with - x.

Result is not a equivalent equation, so symmetric with respect y - axis is failed.

Origin : Replace y with - y and x with - x.

Result is a equivalent equation, so symmetric with respect origin.

To find the x - intercept, substitute y = 0 in the original function.

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The functuion is .

To find the y - intercept, substitute x = 0 in the original function.

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The function is .

Apply first derivative with respect to x.

Apply second derivarive with respect to x.

To find the critical numbers, or does not exist.

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Relative extrema :

If then is called relative maximum of f or f has a relative maximum at .

If then is called relative minimum of f or f has a relative minimum at .

To locate possible points of inflection, determine the values of x for which or does not exist.

does not exit at , so the points of inflection are .

If x = c = 3 then , and points of inflection is (3, 0).

If x = c = - 3 then , and points of inflection is (- 3, 0).

intervals at which the function is increasing and decreasing.

To locate possible points of inflection, determine the values of x for which or does not exist.

does not exit at , so possible points of inflection at .

intervals at which the function is concave up and concave down.

intervals at which the function is concave up and concave down.

Make the table, Choose different values of x and obtain random y - values.intervals at which the function is increasing and decreasing.

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

\ x \	\ \	\ (x, y) \
\ - 4 \	\ \	\ imaginary \
\ - 3 \	\ \	\ \
\ - 2 \	\ \	\ \
\ - 1 \	\ \	\ \
\ 0 \	\ \	\ (0, 0) \
1	\ \	\ \
2	\ \	\ \
3	\ \	\ \
4		imaginary

\

Draw a coordinate plane.

Plot the points and connected these points with a smooth curve.

Observe the graph, the domain is and range is .

Find the all asymptotes :

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