of tems 6 to 10 , use the function \( R(x)=\frac{x^{2}-3 x+2}{x^{2}+2 x-8} \) Find the domain, asymptotes, and intercepts of \( R \).

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

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

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

The range of the function \( f(x)=4 \tan ^{-1}\left(\frac{x}{2}\right) \) is

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.