Question

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. Group of answer choices
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.

Answer 1

Answer:

The correct option is;

E. The whale touches the surface at the maximum

Please find attached the whale motion diagram

Step-by-step explanation:

The given function is f(x) = -4·x²

Therefore, we have;

x,            f(x)

-5,           -100

-4,           -64

-3,           -36

-2,           -16

-1,              -4

0,                0

1,               -4

2,              -16

3,              -36

4,              -64

5,              -100

Which is the gives the singular maximum value for f(x) at x = 0, which is the surface of the water where the whale reaches for air

The errors in the other options are

A. The domain is always real

B. The range is (-∞, 0)

C. There is only one point where the whale touches the surface at x = 0

D. The values of f(x) initially rises, hen descends as the whale moves to the surface of the water and then descends.