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

UESTION 3 On the interval \( [-2,3] \), the maximum vertical distance between the line \( y=x+6 \) and the parabola \( y=x^{2} \) is equal to

\( f(\mathrm{x})=\frac{4 \mathrm{x}}{\mathrm{x}-5} \) 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

Follow the seven step strategy to graph the following rational function. \( f(x)=\frac{4 x}{x-5} \) To graph the function, first determine the symmetry of the graph of f. Choose the correct answer below. origin symmetry neither \( y \)-axis symmetry nor origin symmetry A. The \( y \)-intercept is (Type an integer or a simplified fraction.) B. There is no y-intercept. What is/are the x-intercept(s)? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The x-intercept(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

On the interval \( [-3,4] \), the maximum vertical distance between the line \( y=x+12 \) and the parabola \( y=x^{2} \) is equal to