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

21) \( f(x)=\frac{\frac{-4}{(x-2)^{7}}}{\left(x^{2}-4 x+4\right) \text { or } \quad \frac{-4}{(x-2)(x-2)}} \) \( x \) intercept: \( \quad \) none \( y \) intercept: \( \quad(0,2) \) VA : HA : Holes:

\begin{tabular}{l} (c) \( f(x)=-x(x-3)(5 x+2) \) \\ Falls to the left and rises to the right \\ Rises to the left and falls to the right \\ Falls to the left and falls to the right and rises to the right \\ \hline\end{tabular}

The population of Sasquatch in Salt Lake County was modeled by the function \( P(t)=\frac{400 t}{t+40} \), where \( t=0 \) represents the year 1803 . When were there fewer than 200 Sasquatch in Salt Lake County? Present your answer, to the nearest whole year, in interval notation. There were fewer than 200 Sasquatch in Salt Lake City between the years

Suppose that the function \( h \) is defined on the interval \( (-2,2] \) as follows. \[ h(x)=\left\{\begin{array}{ll}-1 & \text { if }-2<x \leq-1 \\ 0 & \text { if }-1<x \leq 0 \\ 1 & \text { if } 0<x \leq 1 \\ 2 & \text { if } 1<x \leq 2\end{array}\right. \] Find \( h(-1), h(-0.5) \), and \( h(1) \). \( h(-1)=\square \) \( h(-0.5)=\square \)

The relationship between the cone's vertex angle, \( \theta \), and the Mach number, \( m \), of an aircraft that is flying faster than the speed of sound is given by the formula below. If \( \mathrm{m}=\frac{4}{3} \), determine the angle \( \theta \). \( \sin \frac{\theta}{2}=\frac{1}{m} \)