Follow the steps for graphing a rational function to graph the function \( R(x)=\frac{x+2}{x(x+13)} \) A. \( \{x \mid x<\quad\} \) (Type an integer or a simplified fraction.) B. \( \{x \mid x \geq \quad\} \) (Type an integer or a simplified fraction.) D. The domain is the set of all real numbers. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) Write \( R(x) \) in lowest terms. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( R(x)=\square \) (Simplify your answer.) B. \( R(x) \) is already in lowest terms.

3. Plot the points \( A(-2,-3), B(-2,0) \), and \( C(-2,4) \), and verify the following equations by numerical substitutions \[ \overrightarrow{A C}+\overrightarrow{C B}=\overline{A B}, \quad \overline{B A}+\overrightarrow{A C}=\overrightarrow{B C}, \quad \overline{A B}+\overrightarrow{B C}=\overrightarrow{A C} \]

\( (\mathrm{fg})(\mathrm{x})=\square \) (Simplify your answer.)

Compute the discriminant. Then determine the number and type of solutions for the given equation. \( 3 x^{2}+3=0 \) A. two real rational solutions B. one (repeated) real rational solution C. two imaginary solutions D. two real irrational solutions

Solve the equation by the method of your choice. \[ 3 x^{2}-4 x=4 \] The solution set is \( \} \). (Simplify your answer, including any radicals and \( i \) as needed. Use integers or fractions for any numbers in the expression. Use answers as needed.)

In each of Exercises \( 4-12 \). plot the pairs of points and find the distance between them. \( \begin{array}{ll}\text { 4. }(3,1),(7,4) & \text { 5. }(4.137,-2.394),(-8,419,2.843) \\ \text { 5. }(2,3),(-1,0) & \text { 7. }(13,-4),(0,0) \\ \text { 8. }(0,4),(-3,0) & 9 .(-1, \sqrt{2}),(3,-\sqrt{2}) \\ \text { 10. }(6,3),(-1,-1) & \text { 11 }(3,2),(-5,1) \\ \text { 12. }(-3,-3),(2,2) & \end{array} \)