Question

A food packet is dropped from a helicopter and is modeled by the function f(x) = -12x2 + 19200. The graph below shows the height f(x), in feet, of the food packet at different times x, in seconds:

Use the graph to determine the reasonable domain of f(x) based on the context.

all real numbers

x ≤ 19200

-40 ≤ x ≤ 40

0 ≤ x ≤ 40

Answer 1

0 ≤ x ≤ 40

Explanation:

From the graph, we can see the y-intercept is also the maximum. This means that x=0 is our first number. Next, find what x is equal to when the package hits the ground (when y=0). On the graph you can see that y=0 when x=40, this is our second number. Given your choices, it should be clear what the correct answer is.

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Answer 2

For this case we have the following function:

`f(x) = -12x^2 + 19200`
When the food package is on the plane, we have that the height of the package is given by:

`f (0) = -12 (0) ^ 2 + 19200`
Rewriting we have:

`f (0) = 0 + 19200 f (0) = 19200`
When, time passes, the height decreases.
When the time is 40 seconds (x = 40) the package reaches the ground and the height is 0.
Therefore, a reasonable domain for the function is:
0 ≤ x ≤ 40
Answer:
0 ≤ x ≤ 40