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?

Step 2 of 2 : Determine the domain and range of the original function. Express your answer in interval notation.

Step 4 of 4 : Determine the domain and range of the given function. Express your answer in interval notation.

\( \begin{array}{l}\text { Mathematics } \\ \text { Paper } 1 \& \text { Paper } 2\end{array} \) 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 \( y=-1 \)

\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}

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