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: \( 1 \quad \) Shift two units to the left \( 2 \quad \) Shift 3 units up

4. Solve the recurrence relation an \( -80 n-1-16 n-2 \) for \( n \geq 2, a_{0}=16, a_{1}=80 \).

What is the range of the inverse function for the function \( f(x) = \sqrt{x - 4} + 1 \)?

\( 1!+3!+5!+7!+\ldots+2017! \) toplamının birler basamağındaki ra- kam kaçtır? \( \begin{array}{lllll}\text { A) } 9 & \text { B) } 7 & \text { C) } 5 & \text { D) } 4 & \text { E) } 2\end{array} \)

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

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 \( t=2\pi \)).