Find all the complex roots. Write the answer in exponential form. The complex cube roots of \( 3+3 i \). The complex cube roots are (Simplify your answers. Type exact answers, using \( \pi \) as needed. Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than \( 2 \pi \). Use integers or fractions f any numbers in the expression. Use a comma to separate answers as needed.)

Consider the following. \[ g(x)=\frac{x^{2}-2 x-35}{x^{2}-36} \] (a) State the domain of the function. (b) Identify all intercepts. (c) Find any vertical and horizontal asymptotes or holes. (d) Plot additional solution points as needed to sketch the graph of the rational function.

257. Funksiýalaryň grafigini guruñ: \( \begin{array}{ll}\text { a) } y=x^{2}+6 x ; & \text { c) } y=0,5 x^{2}-4 \\ \text { b) } y=-\frac{1}{2} x^{2}+2 ; & \text { d) } y=\frac{1}{2} x^{2}-3 x\end{array} \)

Постройте график функции и укажите для нее область определения и значения \( x \), при которых \( y>0 \). а) \( у=3 \mathrm{x}^{-3} \);

Consider the following. \[ \begin{array}{l}g(x)=\frac{6(x+3)}{x(x-6)} \\ \text { (a) State the domain of the function. } \\ \text { all real numbers } x \text { except } x=3 \text { and } x=6 \\ \text { all real numbers } x \text { except } x=0 \text { and } x=6 \\ 0 \text { all real numbers } x \text { except } x=-3 \text { and } x=6 \\ 0 \text { all real numbers } x \text { except } x=0 \text { and } x=3 \\ \text { all real numbers } x \\ \text { (b) Identify all intercepts. (If an answer does not exist, enter DNE.) } \\ x \text {-intercept } \quad(x, y)=(\square)\end{array} \] \( y \)-intercept \( \quad(x, y)=(\square) \)

Consider the following. \[ \begin{array}{l}g(x)=\frac{5 x}{x^{2}+4 x-5} \\ \text { (a) State the domain of the function. } \\ \text { all real numbers } x \text { except } x=5 \\ \text { all real numbers } x \text { except } x=1 \\ \text { all real numbers } x \text { except } x=-5 \\ \text { all real numbers } x \text { except } x=-5 \text { and } x=1 \\ \text { (b) Identify all intercepts. (If an answer does not exist, enter DNE.) } \\ x \text { except } x=0 \\ x \text {-intercept } \quad(x, y)=(\square) \\ y \text {-intercept } \quad(x, y)=(\square)\end{array} \]