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

\( \begin{array}{l}\text { Mathematics } \\ \text { Paper } 1 \& \text { Paper } 2\end{array} \) QUESTION 3 The equation of a hyperbola is given by \( f(x)=\frac{3}{x-7}-4 \). Write down the equation of the new function that is formed when \( f \) is transformed as follows: 3.1 Shift two units to the left 3.2 Shift 3 units up 3.3 Shift 1 unit right and 2 units down 3.4 The equation of the new hyperbola has new asymptotes at \( x=-4 \) and \( y=-1 \)

2. Esboce o gráfico da função \( f:[0,3] \longrightarrow[-2,10] \) dada por \( f(x)=x^{2}+x-2 \). Verifique se \( f \) é invertível. Se o for, determine sua inversa \( f^{-1} \). 3. Mostre que dentre todos os retângulos de mesmo perímetro o de maior área é o qua- drado.

Consider the following function. \[ m(x)=\frac{1}{x+2}-2 \] Step 1 of 4 : Determine the more basic function that has been shifted, reflected, stretched, or compressed. Answer

\begin{tabular}{l} Use a calculator to approximate the following to five decimal places. \\ \( \frac{\pi^{e}}{e^{\pi}}=\square \) \\ Submit Question \\ \hline Question 9\end{tabular}

\( y = \frac { \sqrt { 2 x - 1 } } { 3 x ^ { 2 } - 1 } \quad [ \frac { 1 } { 2 } \leq x \)