Question

Question 16(Multiple Choice Worth 1 points) (09.01) 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: graph of function f of x equals 19200 minus 12 multiplied by x squared 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.

Hope I helped! ( Smiles )

Answer 2

The reasonable domain of f(x) based on the context:

0 ≤ x ≤ 40

Explanation:

The domain of a function is the collection of all the x-values where the function is defined.

We are given a modelling function f(x) which denotes the height f(x), in feet, of the food packet at different times x,in seconds by:

`f(x)=-12x^2+19200`

The independent variable i.e. x has to be greater than or equal to zero.

i.e. x ≥ 0

and also the value of function i.e. f(x) has to be greater than or equal to 0

( because the packet will either reach the ground i.e. f(x)=0 or will be at some level above the ground i.e. f(x)>0 )

Hence, we have:

`-12x^2+19200\geq 0\\\\\\i.e.\\\\\\12x^2\leq 19200\\\\i.e.\\\\\\x^2\leq 1600\\\\\\i.e.\\\\\\x\leq 40`

Also, by the graph we have to check all those x where the function function is greater than equal to zero and also x≥0.

Hence, the domain of the function is:

0 ≤ x ≤ 40