Question

A ball is dropped from the top of a building that is 1,000 feet high. Its height, in feet, as a function of the time, x, in seconds, after the ball was dropped, is given by the following equation, ƒ(x) = 1,000 - 16x 2. Which set of numbers is appropriate as the domain for this function?

Answer 1

Height = 1000 Feet

Time taken by the ball to reach ground = √2s/g = √2*1000/10 = √200 = 14.14

Domain means input, the value of seconds here, which can't be smaller than the zero and greater than 14.14 (when it hits the ground)

In short, Your Domain would be: "Every Real number between 0 to 14.14"

Hope this helps!

Answer 2

Answer: The set of domain for the function is 0 ≤ x ≤ 7.906

Step-by-step explanation:

Here, the given function that shows the distance of the ball from the surface after x seconds is,

$f(x) = 1000 - 16x^2$

Since, the height can not  be negative,

⇒ f(x) ≥ 0

$\implies 1000 - 16x^2\geq 0$

$\implies -16x^2 \geq - 1000$

$\implies 16x^2\leq 1000$    ( x > y ⇒ -x < -y)

$\implies x^2 \leq \frac{1000}{16}$

$\implies x\leq \sqrt{{\frac{250}{4} }$

$\implies x\leq 7.906$

Also, x represents time,

⇒ 0 ≤ x,

Thus, the possible values of x are,

0 ≤ x ≤ 7.906

Since, all possible value of x = Domain of f(x)

⇒ Domain of f(x) is 0 ≤ x ≤ 7.906