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 \( \quad(x, y)=(\square) \)

Find \( \|\mathbf{v}\| \). \( \begin{array}{l}\mathbf{v}=9 \mathbf{i}-12 \mathbf{j} \\ \|\mathbf{v}\|=\square \text { (Type an exact answer, using radicals as needed. Simplify your answer.) }\end{array} \)

Determine la forma polar del complejo \( z=-3-\sqrt{3} i \)

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

Write the vector v in the form \( \mathrm{ai}+\mathrm{bj} \), given its magnitude \( \|\mathrm{v}\| \) and the angle \( \alpha \) it makes with the positive \( x \)-axis, \[ \alpha v=45^{\circ} \] \( \mathrm{v}=\square \) (Simplify your answer. Type an exact answer using radicals as needed. Type your answer in the form ai + bj.)

Use the given functions to answer the question. \( \begin{array}{l}f(x)=2^{x} \\ g(x)=x-3 \\ \text { What is the domain of } \frac{f(x)}{g(x)}=\frac{2^{x}}{x-3} \text { ? } \\ \text { A. the set of all real numbers } \\ \text { B. the set of all real numbers greater than } 0 \\ \text { D. the set of all real numbers not equal to } 0 \\ \text { E. the set of all real numbers not equal to } 3\end{array} \) B. thers greater than 3