Question

Water coming out from a fountain is modeled by the function f(x)=-x^2+8x+2 where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds.

What does the average rate of change f(x) from x=1 to x=4 represent?

The water travels an average distance of 3 feet from 1 second to 4 seconds.
The water travels an average distance of 2 feet from 1 second to 4 seconds.
The water rises up with an average speed of 3 feet per second from 1 second to 4 seconds.
The water rises up with an average speed of 2 feet per second from 1 second to 4 seconds.

Answer 1

The water rises up with an average speed of 2 feet per second from 1 second to 4 seconds. The vertical increase from x = 1 to x = 4, on the y(i.e. f(x))-axis, represents an increase in the height of the water, since f(x) represents the height, in feet, of the water from the fountain at different times. Graph included below.