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.
what is a reasonable domain for this function?
a. $-1 \leq t \leq 6$
b. $0 \leq t \leq 6$
c. $0 \leq h \leq 196$
d. $96 \leq h \leq 196$

Explanation:

Step1: Understand Domain Definition

Domain is the set of all possible input values (here, \( t \) - time in seconds) for the function.

Step2: Analyze Time Context

Time \( t \) starts at launch, so \( t = 0 \) (launch time) is the minimum. The projectile hits the ground at \( t = 6 \) (from the graph, when \( h = 0 \)). Negative time doesn't make sense here.

Step3: Evaluate Options

• Option A: \( -1 \leq t \leq 6 \) includes negative time (invalid for launch time).
• Option B: \( 0 \leq t \leq 6 \) uses valid time (launch to landing).
• Option C: \( 0 \leq h \leq 196 \) is range (output, height), not domain.
• Option D: \( 96 \leq h \leq 196 \) is also range, not domain.

Answer:

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