Analyze the graph of the function. \( R(x)=\frac{x+4}{x(x+8)} \) (a) What is the domain of \( R(x) \) ? A. \( \{x \mid x \neq 0 \) and \( x \neq-8 \) and \( x \neq-4\} \) B. \( \{x \mid x \neq 0 \) and \( x \neq-4\} \) C. \( \{x \mid x \neq 0 \) and \( x \neq-8\} \) 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.)

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 \( (0,-3) \)

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.)

Write the complex number in trigonometric form \( r(\cos \theta+i \sin \theta) \), with \( \theta \) in the interval \( \left[0^{\circ}, 360^{\circ}\right) \). \[ -3 \sqrt{3}+3 i \] \( -3 \sqrt{3}+3 i=\square\left(\cos \square^{\circ}+i \sin \square^{\circ}\right) \) (Type the value for \( r \) as an exact answer, using radicals as needed. Type the value for \( \theta \) as an intege as needed.)

Suppose the half-life of a drug in the bloodstream is 9 hours. To the nearest milligram, how much of the drug is left in the bloodstream 20 hours after a 260 milligram dose? 56 milligrams 32 milligrams 190 milligrams 117 milligrams

2- Work out composite functions \( f \circ g \) and \( g \circ f \) for each of the following pairs of functions. \( \begin{array}{ll}\text { (a) } f(x)=x-1 \text { and } g(x)=x^{3} & \text { (b) } f(x)=\sqrt{x} \text { and } g(x)=x-2\end{array} \)