Beginning Algebra With Applications, Chapter 5, 5.5, Section 5.5, Problem 68

A child's height is a function of the child's age. The graph of this function is not linear, because children go through growth spurts as they develop. However, for the graph to be reasonable, the function must be an increasing function (that is, as the age increases, the height increases), because children do not get shorter as they grow older. Match each function described below with reasonable graph of the function.

a. The height of a plane above the ground during take-off depends on how long it has been since the plane left the gate.

During takeoff, the height of the plane is increasing so the graph in III best represents this situation.







b. The height of a football above the ground is related to the number of seconds that have passed since it was punted.

The situation in b best represents the graph in IV because as the ball reaches the maximum height after it was being punted, the ball will start to fall back to the ground.







c. A basketball player is dribbling a basketball. The basketball's distance from the floor is related to the number of seconds that have passed since the player began dribbling the ball.

The situation in c best represents the graph in II since the ball start from a certain height not from the ground because the ball came from the hand of the player.







d. Two children are seated together on a roller coaster. The height of the children above the ground depends on how long they have been on the ride.

The graph I best represent the scenario in d because we know that a roller coaster is a type of a ride with series of ups and downs in order for the passenger to be thrilled.