Décrivez comment un déplacement à droite de 3 unités affecte le graphique de la fonction exponentielle \( f(x) = 2^{x} \).

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 \( t=2\pi \)).

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

4. Найдите область определения функции \( y=1-\sqrt{3 t g \frac{x}{2}-\sqrt{3}} \).

(d) \( \sqrt{1+x^{2}} \)

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.