(a) Use the vertex formula to find the vertex. \( \begin{array}{ll}\text { (b) Find the intervals where } f \text { is increasing and where } f \text { is } \\ \text { decreasing. } \\ \begin{array}{ll}\text { 47. } f(x)=6-x^{2} & \text { 48. } f(x)=2 x^{2}-2 x+1 \\ \text { 49. } f(x)=x^{2}-6 x & \text { 50. } f(x)=-2 x^{2}+4 x+ \\ \text { 51. } f(x)=2 x^{2}-4 x+1 & \text { 52. } f(x)=-3 x^{2}+x-\end{array}\end{array} \).

Question 3 (4 points) What is the range of the inverse function of the function \( f(x)=3-\sqrt{x+1} \) ? a) \( (-\infty,-1] \) b) \( [-1, \infty) \) c) \( [3, \infty) \) d) \( (-\infty, 3] \)

What is the domain of the inverse function of the function \( f(x)=3-\sqrt{x} \). 1 ? a) \( (-\infty, 3] \) b) \( [-1, \infty) \) c) \( (-\infty,-1] \) d) \( [3, \infty) \)

d) \( [3, \infty) \) Question 3 (4 points) What is the range of the inverse function of the function \( f(x)=3-\sqrt{x+1} \) ? a) \( [-1, \infty,-1] \) c) \( [3, \infty) \) d) \( (-\infty, 3] \)

A small lake is stocked with a certain species of fish. The fish population is modeled by the function \( P=\frac{14}{1+4 e^{-0.9 t}} \) where \( P \) is the number of fish in thousands and \( t \) is measured in years since the lake was stocked. (a) Find the fish population after 3 years. (Round your answer to the nearest whole fish.) fish (b) After how many years will the fish population reach 7000 fish? (Round your answer to two decimal places.)

Use technology to find points and then graph the function \( y=\sqrt{x+3}-7 \) following the instructions below. Plot at least four points with integer coordinates that fit on the axes below. Click a point to delete it.