Question

An object was dropped off the top of a building. The function f(x) = -16x^2 + 36 represents the height of the object above the ground, in feet, 2 seconds after being dropped. Find and interpret the given function values and determine an appropriate domain for the function.

a) Given function values: f(2) = 4 feet, f(0) = 36 feet, Domain: x ≥ 0
b) Given function values: f(2) = 36 feet, f(0) = 0 feet, Domain: x ≤ 2
c) Given function values: f(2) = 0 feet, f(0) = 36 feet, Domain: x ≥ 2
d) Given function values: f(2) = 36 feet, f(0) = 4 feet, Domain: x ≤ 0

Answer 1

The function f(x) = -16x^2 + 36 incorrectly gives f(2) as -28 feet, which is not possible for a height. The correct value at f(0) is 36 feet, indicating the initial height of the object. The appropriate domain for the function is x ≥ 0, as time cannot be negative.

Step-by-step explanation:

The function f(x) = -16x^2 + 36 represents the height of an object above the ground x seconds after being dropped from the top of a building. To find the function values for f(2) and f(0), we substitute these values into the function.

• For f(2), we calculate -16(2)^2 + 36, which gives us -16(4) + 36 or -64 + 36, resulting in f(2) = -28 feet. However, this value cannot be correct as the height can't be negative, meaning there may have been a misunderstanding of the function or the problem setup.
• For f(0), we calculate -16(0)^2 + 36, which is 0 + 36, resulting in f(0) = 36 feet. This confirms that the object was dropped from a height of 36 feet.

The appropriate domain for this function is x ≥ 0, since time can't be negative and the object is dropped at time x = 0.