Question

the function d(t) defines a travelers distance from home, in miles, as a function of time, in hours.$d(t) = \

$$\begin{cases}300t + 125, & 0 \\leq t < 2.5 \\\\875, & 2.5 \\leq t \\leq 3.5 \\\\75t + 612.5, & 3.5 < t \\leq 6\\end{cases}$$

$which times and distances are represented by the function? select three options.$square$ the starting distance, at 0 hours, is 300 miles.$square$ at 2 hours, the traveler is 725 miles from home.$square$ at 2.5 hours, the traveler is still moving farther from home.$square$ at 3 hours, the distance is constant, at 875 miles.$square$ the total distance from home after 6 hours is 1,062.5 miles.

Explanation:

Step1: Check starting distance (t=0)

Use $D(t)=300t+125$: $D(0)=300(0)+125=125$ miles.

Step2: Check distance at t=2

Use $D(t)=300t+125$: $D(2)=300(2)+125=725$ miles.

Step3: Check movement at t=2.5

At $2.5 \leq t \leq 3.5$, $D(t)=875$ (constant, not moving).

Step4: Check distance at t=3

At $2.5 \leq t \leq 3.5$, $D(t)=875$ miles (constant).

Step5: Check distance at t=6

Use $D(t)=75t+612.5$: $D(6)=75(6)+612.5=450+612.5=1062.5$ miles.

Answer:

B. At 2 hours, the traveler is 725 miles from home.
D. At 3 hours, the distance is constant, at 875 miles.
E. The total distance from home after 6 hours is 1,062.5 miles.