The equation below models the height in feet, h, of a softball t seconds after it is hit by a batter.

Question

h = negative 16 t squared + 105 t + 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.

Answer 1

The height of the ball is a function of time because each value of time is associated with exactly one height. In mathematical terms, a function is defined such that for each input (in this case, time \( t \)), there is a unique output (the corresponding height \( h \)).

In the equation \( h = -16t^2 + 105t + 3 \), if you substitute a specific value of \( t \), you will calculate exactly one value of \( h \). Thus, this attribute satisfies the definition of a function.