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

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

\( f(\mathrm{x})=\frac{4 \mathrm{x}}{\mathrm{x}-5} \) Follow the seven step strategy to graph the following rational function. Find the vertical asymptote(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. B. There is no vertical asymptote. (Type an equation. Use a comma to separate answers as needed.) Find the horizontal asymptote(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The equation(s) of the horizontal asymptote(s) is/are (Type an equation. Use a comma to separate answers as needed.) Blot points between and beyond each \( x \)-intercept and vertical asymptote. Find the value of the function at the given value of \( x \).

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

Use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. \( f(x)=6 x^{4}+7 x^{3}-x+5 \) A. The graph of \( f(x) \) rises to the left and rises to the right B. The graph of \( f(x) \) falls to the left and falls to the right. C. The graph of \( f(x) \) falls to the left and rises to the right D. The graph of \( f(x) \) rises to the left and falls to the right. A

If \( f(x)=3^{x^{2}-4}+4 \), what is the value of \( f(-3) \), to the nearest thousandth (if necessary)?