Question

How do i find the range and domain? please leave detailed steps because i'm struggling with this :(

Answer 1

Check the picture below.

so, mount Rainier is 5400 feet above sea level, and the hiker is going from there, to mount Muir.

now, at 0 hours, the hiker is 5400 feet above sea level, because is on mount Rainier, and every "t" hour passing by, she's going up, according to the equation, 1000 feet, so she does 1000 feet every passing hour.

the domain, INPUT, is from 0, up to whatever long it takes her to get to mount Muir, so from 5400 to 10,100 is 4700 feet, now, she does 1000 every hour, so is 4 hours and 0.7 or 42 minutes, so she'd take 4 hours and 42 minutes.

So the domain will be, from the time she starts at 0 up to 4.7 hours or 4hr and 42mins later.  And in interval notation [0, 4.7].

The range, is how much she went up, well, we checked the difference already, is 4700 feet, so it went from 5400 to 10,100, so the range is just that, 4700 feet, or in interval notation [5400, 10,100]