Question

The height in feet, h, of a projectile above the ground at t seconds from launch can be described by the function shown in the graph.



A graph.Short description, A graph.,Long description,
A coordinate plane shows that t is the horizontal axis and h is the vertical axis. On the coordinate plane, a parabola opens down with a vertex at (2.5, 196), and crosses the vertical h-axis at (0, 96) and crosses the horizontal t axis at (negative 1, 0) and (6, 0).

Question
What is a reasonable domain for this function?

Answer options with 4 options
A.
negative 1 is less than or equal to t which is less than or equal to 6

B.
0 is less than or equal to t which is less than or equal to 6

C.
0 is less than or equal to h which is less than or equal to 196

D.
96 is less than or equal to h which is less than or equal to 196

Answer 1

To determine a reasonable domain for the height function \( h(t) \) based on the description of the projectile's motion, we need to consider the values of \( t \) (time in seconds) for which the projectile is in the air.

From the description:
- The projectile is launched at \( t = 0 \) and it hits the ground (where \( h = 0 \)) at \( t = -1 \) and \( t = 6 \).

However, since time cannot be negative in the context of projectile motion, we disregard \( t = -1 \) as an unrealistic situation. Thus, the realistic time range for which the projectile is in the air is between \( t = 0 \) seconds and \( t = 6 \) seconds.

Therefore, the reasonable domain for this function is:

**A.** \( -1 \leq t \leq 6 \) (but since \( t \) cannot be negative, we focus only on the range where \( 0 \leq t \leq 6 \)).

The most appropriate answer among the given options is:

**B.** \( 0 \leq t \leq 6 \)