Analyze the graph of the function. \( R(x)=\frac{3 x+3}{7 x+21} \) (a) What is the domain of \( R(x) \) ? A. \( \{x \mid x \neq 0 \) and \( x \neq-3\} \) B. \( \{x \mid x \neq 0 \) and \( x \neq-3 \) and \( x \neq-1\} \) C. \( \{x \mid x \neq-3\} \) D. All real numbers (b) What is the equation of the vertical asymptote(s) of \( R(x) \) ? Select the correct choice below and fill in any answer boxes within your choice. A. \( x=\square \) (Use a comma to separate answers as needed. Type an integer or a fraction.)

Write the complex number in trigonometric form \( r(\cos \theta+i \sin \theta) \), with \( \theta \) in the interval \( \left[0^{\circ}, 360^{\circ}\right) \). \[ \begin{array}{l}1+i\end{array} \] \( \begin{array}{l}1+i=\square\left(\cos \square^{\circ}+i \sin \square^{\circ}\right) \\ \text { (Type the value for } r \text { as an exact answer, using radicals as needed. Type the value for } \theta \text { as an integer or } \\ \text { as needed.) }\end{array} \)

Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci at \( (0,-8) \) and \( (0,8) \); vertices at \( (0,3) \) and \( (0,-3) \)

Follow the seven step strategy to graph the following rational function. \( f(x)=\frac{6 x}{x-3} \) Find the horizontal asymptote(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The equation(s) of the horizontal asymptote(s) is/are (Type an equation. Use a comma to separate answers as needed.) B. There is no horizontal asymptote.

Find the magnitude and positive direction angle of the vector \( \langle 2,-2 \sqrt{3}\rangle \). The magnitude of the vector is (Simplify your answer.)

The exponential model \( \mathrm{A}=612.2 e^{0.014 t} \) describes the population, A, of a country in millions, \( t \) years after 2003. Use the model to determine when the population of the country will be 724 million. The population of the country will be 724 million in (Round to the nearest year as needed.)