Question

Tina was observing the changing heights of a ball as it bounced over time. She graphed the function on this coordinate grid to show f(x), the height of the dropped ball, in feet, after its xth bounce.

Part A: What does the value of f(3) represent in the given context?


A.

After 4 bounces the height of the ball is 3 feet.


B.

After 3 bounces the height of the ball is 4 feet.


C.

After 4 bounces the height of the ball is 4 feet.


D.

After 3 bounces the height of the ball is 3 feet.



Part B: Tina said that a possible range for the given function is y > 0. Based on the given scenario, do you agree or disagree?


A.

I disagree; because the graph has an asymptote at y = 0, the height cannot be 0.


B.

I disagree; although the graph has an asymptote at y = 0, the ball will stop bouncing and have a height of 0.


C.

I agree; although the graph has an asymptote at y = 0, the ball will stop bouncing and have a height of 0.


D.

I agree; because the graph has an asymptote at y = 0, the height cannot be 0

Answer 1

Explanation:

Part A:

The value of f(3) represents the height of the ball after its 3rd bounce.

From the graph, we can see that the point corresponding to the 3rd bounce has a height of 4 feet.

Therefore, the correct answer is B. After 3 bounces, the height of the ball is 4 feet.

Part B:

The given function represents the height of the ball after each bounce. Since the ball is bouncing, its height will always be greater than zero.

The graph shows that the function has an asymptote at y = 0, which means that the height of the ball will approach zero as it bounces. However, this does not mean that the ball will never have a height of zero. The ball will eventually stop bouncing and come to rest on the ground, which corresponds to a height of zero.

Therefore, the correct answer is C. We agree that a possible range for the given function is y > 0.