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

the function d(t) defines a travelers distance from home, in miles, as a function of time, in hours. d(t) = { 300t + 125, 0 ≤ t < 2.5; 875, 2.5 ≤ t ≤ 3.5; 75t + 612.5, 3.5 < t ≤ 6 } which times and distances are represented by the function? select three options. the starting distance, at 0 hours, is 300 miles. at 2 hours, the traveler is 725 miles from home. at 2.5 hours, the traveler is still moving farther from home. at 3 hours, the distance is constant, at 875 miles. 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. d(t) = { 300t + 125, 0 ≤ t < 2.5; 875, 2.5 ≤ t ≤ 3.5; 75t + 612.5, 3.5 < t ≤ 6 } which times and distances are represented by the function? select three options. the starting distance, at 0 hours, is 300 miles. at 2 hours, the traveler is 725 miles from home. at 2.5 hours, the traveler is still moving farther from home. at 3 hours, the distance is constant, at 875 miles. the total distance from home after 6 hours is 1,062.5 miles.

Answer

Explanation:

Step1: Check starting - distance

For (t = 0), since (0\leq t<2.5), we use (D(t)=300t + 125). Substitute (t = 0) into the function: (D(0)=300\times0+125 = 125) miles, so the statement "The starting distance, at 0 hours, is 300 miles" is false.

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) miles. So the statement "At 2 hours, the traveler is 725 miles from home" is true.

Step3: Analyze (t = 2.5)

For (2.5\leq t\leq3.5), (D(t)=875). At (t = 2.5), the function value changes from the linear - increasing part to a constant part, so the traveler is not moving farther from home at (t = 2.5) hours. The statement "At 2.5 hours, the traveler is still moving farther from home" is false.

Step4: Analyze (t = 3)

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

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) miles. So the statement "The total distance from home after 6 hours is 1,062.5 miles" is true.

Answer:

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