the function d(t) defines a travelers distance from home, in miles, as a function of time, in…

the function d(t) defines a travelers distance from home, in miles, as a function of time, in hours.\nd(t)=\begin{cases}300t + 125, &0leq t<2.5\\875, &2.5leq tleq3.5\\75t + 612.5, &3.5<tleq6end{cases}\nwhich times and distances are represented by the function? select three options.\n□ the starting distance, at 0 hours, is 300 miles.\n□ at 2 hours, the traveler is 725 miles from home.\n□ at 2.5 hours, the traveler is still moving farther from home.\n□ at 3 hours, the distance is constant, at 875 miles.\n□ the total distance from home after 6 hours is 1,062.5 miles.

the function d(t) defines a travelers distance from home, in miles, as a function of time, in hours.\nd(t)=\begin{cases}300t + 125, &0leq t<2.5\\875, &2.5leq tleq3.5\\75t + 612.5, &3.5<tleq6end{cases}\nwhich times and distances are represented by the function? select three options.\n□ the starting distance, at 0 hours, is 300 miles.\n□ at 2 hours, the traveler is 725 miles from home.\n□ at 2.5 hours, the traveler is still moving farther from home.\n□ at 3 hours, the distance is constant, at 875 miles.\n□ the total distance from home after 6 hours is 1,062.5 miles.

Answer

Explanation:

Step1: Check starting distance

When (t = 0), use (D(t)=300t + 125). Substitute (t = 0) into the function: (D(0)=300\times0+125 = 125\neq300).

Step2: Calculate distance at (t = 2)

Since (0\leq t<2.5), use (D(t)=300t + 125). Substitute (t = 2) into the function: (D(2)=300\times2+125=600 + 125=725).

Step3: Analyze (t = 2.5)

When (t = 2.5), the function changes to (D(t)=875). Before (t = 2.5), the function is (D(t)=300t + 125), and at (t = 2.5), the value jumps to 875, so the traveler is not moving farther from home at (t = 2.5).

Step4: Analyze (t = 3)

Since (2.5\leq t\leq3.5), (D(t)=875). So at (t = 3), the distance is constant at 875 miles.

Step5: Calculate distance at (t = 6)

Since (3.5<t\leq6), use (D(t)=75t + 612.5). Substitute (t = 6) into the function: (D(6)=75\times6+612.5=450+612.5 = 1062.5).

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.