Question

A food packet is dropped from a helicopter and is modeled by the function f(x) = −15x2 + 6000. The graph below shows the height f(x), in feet, of the food packet at different times x, in seconds: graph of function f of x equals 6000 minus 15 multiplied by x squared Use the graph to determine the reasonable domain of f(x) based on the context. x ≤ 6000 0 ≤ x ≤ 20 −20 ≤ x ≤ 20 All real numbers

Answer 1

answer is B

Explanation:

Answer 2

General Idea:

Domain of a function means the values of x which will give a DEFINED output for the function.

Applying the concept:

Given that the x represent the time in seconds, f(x) represent the height of food packet.

Time cannot be a negative value, so

`x\geq 0`

The height of the food packet cannot be a negative value, so

`f(x)\geq 0`

We need to replace
`-15x^2+6000` for f(x) in the above inequality to find the domain.

`-15x^2+6000\geq 0 \; \; [Divide \; by\; -15\; on\; both\; sides]\\ \\ (-15x^2)/(-15) +(6000)/(-15) \leq (0)/(-15) \\ \\ x^2-400\leq 0\;[Factoring\;on\;left\;side]\\ \\ (x+200)(x-200)\leq 0`

The possible solutions of the above inequality are given by the intervals
`(-\infty , -2], [-2,2], [2,\infty )`. We need to pick test point from each possible solution interval and check whether that test point make the inequality
`(x+200)(x-200)\leq 0` true. Only the test point from the solution interval [-200, 200] make the inequality true.

The values of x which will make the above inequality TRUE is
`-200\leq x\leq 200`

But we already know x should be positive, because time cannot be negative.

Conclusion:

Domain of the given function is
`0\leq x\leq 200`