The function f(x) = –4x2 represents the path of a whale as it surfaces for air and dives again. Select all the observations that are true about the whale’s path. A. The domain is all real numbers x until the ocean hits the shore.

B. The range is (−∞,−4)

C. There are two points where the whale touches the surface.

D. f is decreasing for the whale's entire path.

E. The point where the whale touches the surface is a maximum.

Option (A) and (E)

Step-by-step explanation:

Characteristics of the quadratic function representing the path of a whale as it surfaces for air is,

y = -4x²

1). Since domain of the given function will be all real number x until ocean hits the shore on both the sides of the path.

2). Range of the function will be the value of y from the bottom of the ocean to the surface.

3). Whale will touch the surface of the ocean at one point only.

4). Function 'f' will increase initially upto the surface of the ocean and then it will decrease.

5). Point where the hale touches the surface will be maximum.

Therefore, Options (A) and (E) will be the correct options.

answer4 to the second power is 16

and 4 to the third power is 64,