Draw a graph of \( f(x)=\frac{3 x+6}{x+1} \) by first placing the horizontal and vertical asymptotes, then plotting an additional point on the graph.

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.

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

7. The graph of \( f(x)=80 \cdot(0.5)^{x} \) is shown. Tasha believes that the graph touches the \( x \)-axis while Greg believes that it doesn't. Who is correct, and how do you know?

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) \( \operatorname{coth}(\ln (6)) \)