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:

Question

anonymous · Answer

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

phi · Answer

x is the time since the food was dropped from the helicopter.

at time 0  (x=0) , the food is at 19200 feet.

they want *a reasonable domain of f(x) *
the domain are the "legal" x values.

do you think we should include negative time  (x < 0) ?  the graph shows the food zooming up to the helicopter.... which we know it does not do.  So it makes sense to say, we will not use x<0 .  Also, after the food hits the ground, it does not continue burrowing into the earth.. so we want to exclude that part of the curve also.

any ideas what the domain should be ?

anonymous · Answer

-40?

phi · Answer

what x values should you use ?  It will be a range... not just a single number.

phi · Answer

How about the x values that show from the time the food is dropped until the food hits the ground ?

anonymous · Answer

there all real?

phi · Answer

the first choice *all real numbers*  means x can be -10  or +50 for example.
If you look at your graph,  the curve does not show the height of the food at those points
For example at x=50,  the food is 10000 feet below the surface of the earth.  You do not want to allow x=50, because the curve is giving you the wrong answer there