In a previous investigation we thought about tossing a ball up into the air and tracking the ball's height above the ground as a function of the elapsed time since the ball was thrown. h represents the ball's height above the ground (in feet) t represents the elapsed time since the ball was thrown (in seconds) h is a function of t , and we will call this function f . So f ( t ) = h . t f ( t ) 0 0 0.3 18.12 0.62 31 1.2 37.92 1.57 31 1.7 26.52 One of your friends said that we can create the inverse function f 1 ( h ) = t , which inputs the ball's height above the ground (in feet) and outputs the time elapsed (in seconds) since the ball was thrown. Therefore, we can write statements like: f 1 ( 31 ) = 0.62 , which means that when the ball is 31 feet above the ground, 0.62 seconds have passed since the ball was thrown and f 1 ( 26.52 ) = 1.7 , which means that when the ball is 26.52 feet above the ground, 1.7 seconds have passed since the ball was thrown. Do you agree with your friend? Take a second to think about this, and then continue reading. He or she is not correct only because the inverse relationship is not a function. When given the height of the ball above the ground in feet we can't know exactly how much time has elapsed since the ball was thrown (most heights have two different elapsed times associated with them). Since using a height above the ground to determine the time elapsed is a not a function relationship it is incorrect to use function nota