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.)

Find an equation for the hyperbola described. Graph the equation. Center at \( (-1,-7) ; \) focus at \( (-1,-10) ; \) vertex at \( (-1,-9) \) Write an equation for the hyperbola. \( \square-\square=1 \) (Type exact answers for each term, using fractions as needed.)

The size of a certain insect population is given by \( \mathrm{P}(\mathrm{t})=400 e^{.03 \mathrm{t}} \), where t is measured in days. At what time will the population equal 1600 ?

What is the direction of a vector with a horizontal component of 2 and a vertical component of -4 ?

Where is there a discontinuity / are there discontinuities (holes or asymptotes) in the rational function \( f(x)=\frac{x^{2}+3 x+2}{x^{2}-4} ? \) \( x= \) 0 \( x= \) 2 \( x= \) -2 \( x=2 \) -2 \( x=0 \) \( 2,-2 \) \( x \)

Select your answer What is the direction of a vector with a horizontal component of -2 and a vertical component of -4 ? \( -63^{\circ} \) \( -117^{\circ} \) 0.