Question

if traveling at a constant pace, 50 miles in the first hour, 255 miles in the next 3 hours, and 120 miles in the next 2 hours, create a piecewise function representing the traveling time and distance, what does domain mean in the context of the situation and identify, what does range mean in the context of the situation and identify, what assumptions are being made in the context of the situation, explain?????? I'm confused

Answer 1

Do you see why you need to use a piecewise thing? each segment has a constant pace (slope) , and they are not the same

Answer 2

This is what I assume is the piecewsie part

distance traveled = 50t when 0 < t ≤ 1
= 50 + 85t when 1 < t ≤ 4
= 50 + 255 + 60t when 4 < t ≤ 6

Answer 3

yes each part represents a line segment over that interval, the slope is the rate, miles per hour, the starting point is the end point of the previous segment

Answer 4

put them like this for each segment

Answer 5

a couple things, time can be zero, for the first equation, use greater than or equal to zero, at t=0, distance is zero

Answer 6

the starting point for the third line is when t=4 from the last line, 85*4+50 = 390

third line is then 60t+390

Answer 7

insert the time intervals after each if, then done

Answer 8

good on tha tpart?

Answer 9

ok, thanks I understand that part alot better now. but what about explaining the domain, range, and context that's what's really confusing me I don't understand what it means

Answer 10

the domain is all the possible values for t
the range is the possible values of D(t) resulting from the domain

Answer 11

in this real world situation, his rate changes instantaneously for each change in his rate, that is impossible, you would need an infinite acceleration

Answer 12

a real world graph would be curved and no longer linear

Answer 13

instead of sharp points where the slopes change

Answer 14

Ok Thank you so much I think I understand it better now

Answer 15

welcome, try to graph it

the slope is the velocity