Question

A comet travelling through space at a rate of 75 miles per hour has just flown into a huge amount of space dust. This dust decreases the speed of the comet by 15 miles every hour, until it completely stops moving. Which are the domain and range of the linear function that represents this relationship?

Answer 1

domain is 0,5

Explanation:

after 5 hours, it stops moving

Answer 2

Linear function: y = -15x + 75

Domain: x ≤ 5

Range: y ≥ 0

Please tell me if there are any mistakes in my answer and I will correct them.

Explanation:

The linear function is y = -15x + 75, written in y=mx+b form. X is the amount of hours. Since the speed is decreasing, we will use -15. Since we started at 75 miles per hour, our b value will be 75.

Domain

The domain is all the possible values for x.

Since the comet slows down by 15 miles every hour until it stops moving, we can solve for x by putting in 0 for y.

0 = -15x + 75

15x = 75

x = 5

Therefore, the domain is x ≤ 5.

Range

The range is the set of all possible values of y. In this case, the range can be anything but 0 in order for the equation to make sense.

So, the range is y ≥ 0.