Question

The height
at time
of a ball dropped from 144 feet above the ground is given by the function
. Time is given in seconds and height is measured in feet. This table shows some points on the graph of the function:

0 144
1 128
2 80
3 0

Is the function one-to-one (does it have an inverse that is also a function)?



Responses

Yes
Yes

No
No

Yes, with a restricted domain

Answer 1

Yes — on the physical domain (time t ≥ 0, here 0 ≤ t ≤ 3) the heights decrease strictly, so each height comes from exactly one time. (If the quadratic were allowed for negative t as well, it would not be one-to-one.)