Explica cuál sería el resultado de una compresión vertical en la función exponencial \( h(x) = 5^x \) cuando se multiplica por \( \frac{1}{2} \).

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: \( 3.1 \quad \) Shift two units to the left \( 3.2 \quad \) Shift 3 units up Shift 1 unit right and 2 units down QU.3 The equation of the new hyperbola has new asymptotes at \( x=-4 \) and \( y=-1 \) Sketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and \( g(x)=-2 \cdot 2^{x-1}+1 \)

If \( f(x)=\frac{\sqrt{x+2}}{3-3 x^{2}} \), for which values of \( x \) is 1.2.2 \( \quad f(x) \) non real.

20. Исследовать функцию и построить ее график: \( y=\frac{x^{3}-3 x}{x^{2}-1} \).

- Parametrik tenglamalar bilan berilgan \( x=\sin 2 t, \quad y=\cos 2 t, \quad-\pi / 2<t<\pi / 2 \) egri chiziq Dekart koordinatalar sistemasidagi tenglamasini yozing.

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: \( 3.1 \quad \) Shin two units to the left \( \begin{array}{ll}3.2 & \text { Shift } 3 \text { units up } \\ 3.3 & \text { Shift } 1 \text { unit right and } 2 \text { units down } \\ \text { The equation of the new hyperbola has new asymptotes at } x=-4 \text { and } y=-1\end{array} \)