The equation below models the height in feet, h, of a softball t seconds after it is hit by a batter. h= -16t2+105t+3

Why is the height of the ball a function of time?

- Each value of time is associated with exactly one height.
- Each height of the ball is associated with exactly one moment in time.
- There is exactly one time at which the maximum height is attained.
- There is a maximum and minimum height that the ball can reach.

Question

The equation below models the height in feet, h, of a softball t seconds after it is hit by a batter. h= -16t2+105t+3

Why is the height of the ball a function of time?

- Each value of time is associated with exactly one height. 
- Each height of the ball is associated with exactly one moment in time. 
- There is exactly one time at which the maximum height is attained. 
- There is a maximum and minimum height that the ball can reach.

InsatiableSuffering · Answer

Think about it this way. For an equation to be a function, it must pass the vertical line test. This is to test if a single x value has more than 1 output. If it does, then it fails and is not a function. If it doesn't, then it is a function. In other words, any x value will only return a single y value. Thus, y values are dependent on whatever x value you plug into any equation. Knowing this, which answer choice defines a function?