Question

Will is diving. If w(t) represents the height in feet of Will, at time, t, seconds, and g(t) is a constant function that represents the height of the diving board, what situation can be described by (w + g)(t)? Include a description of the domain.
Responses

The function (w + g)(t) is the height in feet at time, t, seconds of Will diving off the diving board. The domain is all numbers greater than or equal to 0, because time must be zero (the starting time) or higher.
.

The function (w + g)(t) is an addition sum situation. The domain is the derivative of the original function and must equal 0.

The function (w + g)(t) is the amount of time, t, in seconds, it takes Will to reach the water. The domain will be his highest height to 0, which is when he hits the water.


[Choice D]

Answer 1

The function (w + g)(t) represents the height in feet of Will above the water at time t seconds, where w(t) is Will’s height while diving and g(t) is the constant height of the diving board above the water. This function combines both heights to show his total height at any given time during the dive.

The domain of this function would be all non-negative real numbers, specifically \( t \geq 0 \), because time cannot be negative; t starts from the moment Will jumps off the diving board (t = 0) and continues until he reaches the water's surface. Depending on how deep the diving board is above the water and how long the dive takes, the function could have a finite upper limit for t when Will hits the water, but in general, the domain should start from zero.

So, the appropriate option that correctly describes the situation is:

**The function (w + g)(t) is the height in feet at time, t, seconds of Will diving off the diving board. The domain is all numbers greater than or equal to 0, because time must be zero (the starting time) or higher.**