Постройте график функции y=(x^3-2x^2-9x+18)/(18-2x^2).

Ответ:

\[y(x) = \frac{x^{3} - 2x^{2} - 9x + 18}{18 - 2x^{2}} =\]

\[= \frac{x^{2}(x - 2) - 9(x - 2)}{- 2\left( x^{2} - 9 \right)} =\]

\[= \frac{(x - 2)\left( x^{2} - 9 \right)}{- 2\left( x^{2} - 9 \right)} =\]

\[= \frac{x - 2}{- 2} = \frac{2 - x}{2} = 1 - \frac{x}{2};\ \ \ \ \]

\[x \neq \pm 3.\]