Question

question: 7
the graph below shows the height of a basketball after it is thrown towards a basketball hoop.
what is the domain of the above function?
a. 0, 55
b. 0, 6.2
c. 6.2, 10
d. 10, 55

Explanation:

Step1: Understand Domain Definition

Domain of a function (here, height vs. time) is the set of all input values (time, \( t \)) for which the function is defined. From the graph, time starts at \( t = 0 \) (when the basketball is thrown) and ends when the basketball hits the ground (where \( t \) is around 6.2 seconds, as the graph touches the \( t \)-axis there).

Step2: Analyze Options

• Option A: \([0, 55]\) – 55 is a height value (range), not time. Eliminate.
• Option B: \([0, 6.2]\) – Matches the time interval from start (\( t = 0 \)) to when the ball hits the ground (\( t \approx 6.2 \)).
• Option C: \([6.2, 10]\) – Time starts at 6.2, but the ball is thrown at \( t = 0 \). Eliminate.
• Option D: \([10, 55]\) – Both time and height values are incorrect. Eliminate.

Answer:

B. \([0, 6.2]\)