Marie is logging the number of radioactive isotopes she observes every minute. She has determined her function to be f(x) = -4x + 120.
Based on the situation above, describe any necessary restrictions to the domain and range. Provide justification for the restrictions.

Question

Marie is logging the number of radioactive isotopes she observes every minute. She has determined her function to be f(x) = -4x + 120.
Based on the situation above, describe any necessary restrictions to the domain and range. Provide justification for the restrictions.

anonymous · Answer

$$x \in [0, 30]$$
as the number of radioactive isotopes cannot be less than zero or more than 120

unklerhaukus · Answer

Why can't it be more than 120?  (for negative x)

anonymous · Answer

sorry what does that mean, I'm so confused on this question?

anonymous · Answer

@UnkleRhaukus , i think as f is the function of minute x, marie cannot go back to negative time because she will note the number after starting observation, in that case, x has to be greater than or equal to 0

unklerhaukus · Answer

presumably the isotope was (more) radioactive before the observations began, 
i think marie's equation can be use to predict the radioactivity at times before  the measurements started (negative x).

anonymous · Answer

well, i think that's correct

unklerhaukus · Answer

the range of possible observations must be non-negative 

so           f(x)  ≥ 0
     -4x + 120 ≥ 0
                120 ≥ 4x
                  30 ≥ x
                    x ≤ 30