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.

Suppose that the functions \( f \) and \( g \) are defined as follows. \[ \begin{array}{l}f(x)=2 x+3 \\ g(x)=\sqrt{4 x+1} \\ \text { Find } \frac{f}{g} \text { and } f-g \text {. Then, give their domains using interval notation. } \\ \begin{array}{l}\left(\frac{f}{g}\right)(x)=\square \\ \text { Domain of } \frac{f}{g}: \square \\ \text { Domain of } f-g: \square\end{array} \\ \qquad\end{array} \] \( \begin{array}{l}\qquad-g)=\square\end{array} \) \[ \]

Consider the following. \[ f(x)=\frac{x^{2}+4}{x+1} \] (a) State the domain of the function. (b) Identify all intercepts. (c) Find any vertical and slant asymptotes. (d) Plot additional solution points as needed to sketch the graph of the rational function.

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.)

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

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