The function D(t) defines a traveler’s distance from home, in miles, as a function of time, in hours. 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.

[tex]D(t) = 300t \ + \ 125, \ \ \ \ \ 0\leq t\leq 2.5\\\\D(t) = 875, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2.5 \leq t\leq 3.5 \\\\D(t) = 75t + 612.5 , \ \ \ \ \ \ 3.5 \leq t\leq 6 \\\\[/tex]

From the given distance function, we can calculate the distance traveled at each time;

at 0 hours, the starting distance of the traveler is calculated as;

[tex]D = 300(0) + 125\\\\D = 125 \ miles[/tex]

at 2 hours, the distance traveled is calculated as;

[tex]D = 300(2) + 125\\\\D = 725 \ miles[/tex]

at 2.5 hours, the distance traveled by the traveler is calculated as;

[tex]D = 300(2.5) + 125\\\\D = 875 \ miles[/tex]

At 3 hours, the distance traveled by the traveler is calculated as;

[tex]D(t ) = 875 \ \ \ \ \ 2.5 \leq t \leq 3.5\\\\D(3) = 875 \ miles[/tex]

The total distance from home after 6 hours is calculated as follows;

[tex]D = 75(6) \ + \ 612.5\\\\D = 1,062.5 \ miles[/tex]

Thus, the times and distances that represents the travelers motion are;

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.

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