Find the horizontal asymptote, if any, of the graph of the rational function. \( g(x)=\frac{8 x^{2}-2 x-9}{7 x^{2}-4 x+7} \)

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 \( t=2\pi \)).

At which \( x \)-intercept(s) does the graph touch the \( x \)-axis and turn around? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( x=\square \) (Use a comma to separate answers as needed.). B. There are no \( x \)-intercepts at which the graph touches the \( x \)-axis and turns around.

Which of the following functions has an asymptote at \( y=5 \) ? A. \( f(x)=\ln (x+1)+5 \) B. \( f(x)=e^{-x}+5 \) C. \( f(x)=\sqrt{x}+5 \) D. \( f(x)=x^{2}+5 \)

2. Постройте график функции: \( \begin{array}{ll}\text { a) } y=\sqrt{x-1}-1 ; & \text { в) } y=-4(x-2)^{2}-1 \\ \text { б) } y=\frac{4}{x-5}-1 ; & \end{array} \)

Q. 41. Find all asymptotes of the curve \( x^{3}+y^{3}=3 a x y \). (Bhopal 1991, 2000; Sagar