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 noo units to the left 3.2 Shif 3 units up 3.3 Shift 1 unit nght and 2 units down \( 3.4 \quad \) The equation of the new hypertola has new asymplotes at \( x-4 \) and \( y=-1 \)

The population of a certain species in a protected area can be modeled by the function \( P(t) = 200 + 50 \sin(t) \), where \( t \) is measured in years. Determine the total population increase over one complete cycle (from \( t=0 \) to \( t=2\pi \)).

Use generating functions to solve the recurrence relation \( a_{n}-2 a_{n-1}-3 a_{n-2}=0, n \geq 2 \) wisth \( a_{0}=3, a_{1}=1 \).

إذا كانت الدالة \( f(x) = \sqrt{x - 1} \)، فما هو مجال الدالة المعكوسة؟

Verifica si las funciones \( g(x) = \sqrt{x} \) y \( h(x) = x^{2} \) son inversas entre sí usando composición.

UESTION 3 he equation of a hyperbola is given by \( f(x)=\frac{3}{x-7}-4 \). Srite down the equation of the new function that is formed when \( f \) is transformed as follows: .1 Shift two units to the left .3 Shift 3 units up 1 unit right and 2 units down .4 The equation of the new hyperbola has new asymptotes at \( x=-4 \) and \( y=-1 \)