35. La población (en miles) de una colonia de bacterias, \( t \) minutos después de introducir una toxina, está dada por la función \[ f(t)=\left\{\begin{array}{ll}t^{2}+7 & \text { si } t<5 \\ -8 t+72 & \text { si } t \geq 5\end{array}\right. \]

Evaluate the function. If the value is not a rational number, round your answer to three decimal places. (a) \( \operatorname{csch}^{-1}(3) \) (b) \( \operatorname{coth}^{-1}(6) \)

Find any vertical asymptotes. \( h(x)=\frac{(x-3)(x+6)}{x^{2}-4} \)

Graph the rational function. \( f(x)=\frac{-4 x^{2}+12 x+12}{6 x+9} \) Start by drawing the asymptotes. Then plot two points on each piece of the grap

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

Evaluate the function. If the value is not a rational number, round your answer to three decimal places. (a) \( \operatorname{csch}(\ln (4)) \) (b) \( \operatorname{coth}(\ln (6)) \)