\( r = 2 \theta \sqrt { \cos \theta } \)

\( f(x)=\frac{12 x}{7 x^{2}+9} \) Find the horizontal asymptote, if any, of the graph of the rational function. A. The horizontal asymptote is \( \square \). (Type an equation.) B. There is no horizontal asymptote.

An equation for the slant asymptote for the graph of the function \( f(x)=\frac{2 x^{2}-x+3}{x+4} \) is

Suppose that the function \( f \) is defined for all real numbers as follows. \[ f(x)=\left\{\begin{array}{ccc}6 & \text { if } & x<-4 \\ -10+x^{2} & \text { if } & -4 \leq x<4 \\ 2 x-2 & \text { if } & x \geq 4\end{array}\right. \] Graph the function \( f \). Then determine whether or not the function is continuous.

Use the value of the given hyperbolic function to find the values of the other hyperbolic functions. \( \sinh (x)=\frac{5}{4} \) \( \tanh (x)= \) \( \operatorname{csch}(x)= \) \( \operatorname{sech}(x)= \) \( \operatorname{coth}(x)= \)

Find the vertical asymptotes, if any, and the values of \( x \) corresponding to holes, if any, of the graph of the rational function. \( h(x)=\frac{x+3}{x(x-2)} \) A. The vertical asymptote(s) is(are) \( \square \) and hole(s) corresponding to \( \square \) a comma to separate answers as needed.) B. The vertical asymptote(s) is(are) \( \square \). There are no holes. C. There are no vertical asymptotes but there is(are) hole(s) corresponding to \( \square \). D. There are no discontinuities.