Bill Ny, the Science Guy, dropped an egg from the top of a building 20 feet above the ground. The function f(n) = -16n² + 20 gives the height of the egg in feet after n seconds. Determine the range of the function.

1. -∞ < x < ∞
   Incorrect. The domain is connected to the x variable and the range is connected to the y variable.
2. -∞ < y < ∞
   Incorrect. Since the egg was dropped from a 20 foot building the range would not extend to infinity.
3. y ≤ 20
   Incorrect. Since the egg was dropped from a 20 foot building the maximum value for the range is 20, but the egg will land on the ground, y = 0, the minimum value for the range.
4. 0 ≤ y ≤ 20
   Correct! Since the egg started at a height of 20 ft, that would be the maximum range and the minimum range would be y = 0, when the egg touches the ground.

An object is launched straight up into the air at an initial velocity of 50 feet per second. It is launched from a height of 8 feet off the ground. The function f(x) = -16x² + 50x + 8 gives the height of the object in feet after x seconds. Approximate a reasonable domain given the problem situation.

1. -∞ < x < ∞
   Incorrect. The x value represents time, seconds, which is never a negative value.
2. 0 ≤ x ≤ 3.3
   Correct! The domain represents seconds. The rockets initial time in seconds is zero and it will reach the ground in about 3.3 seconds.
3. -∞ < y < ∞
   Incorrect. This inequality could represent the range, not the domain.
4. x ≤ 45
   Incorrect. The minimum value for x is 0 since x represents seconds.

The graph below represents the height of an object falling from a building after x seconds. Given the graph, determine the domain.

1. -2 ≤ x ≤ 2
   Incorrect. The domain, x, is time in seconds. Time is never a negative number.
2. -∞ < x < ∞
   Incorrect. The domain, x, is time in seconds. Time is never a negative number.
3. 0 ≤ x ≤ 2
   Correct! The domain, x, represents time in seconds so it will be 0 or greater. The object lands on the ground in 2 seconds, the maximum value for the range.
4. y ≤ 62
   Incorrect. The domain is the x value.

The graph below represents the height of an object falling from a building after x seconds. Given the graph, determine the range.

1. -∞ < x < ∞
   Incorrect. The domain, x, is time in seconds, not the range.
2. y ≤ 62
   Incorrect. The maximum value for the height of the object is 62, but the minimum height is 0, when it lands on the ground.
3. x ≤ 62
   Incorrect. The domain is the x value, which is not the range.
4. 0 ≤ y ≤ 62
   Correct! From the graph the maximum height of the object is 62 and the minimum height when it lands on the ground is at y = 0.