Choose the graph that best describes the following:
The height of a basketball (Y) when a player bounces it as a function of time (X).
We have hundreds of course questions with personalized recommendations + Account 100% premium
Choose the graph that best describes the following:
The height of a basketball (Y) when a player bounces it as a function of time (X).
When the player dribbles the ball, it starts from hand height and then moves downwards to touch the floor before bouncing up again. This motion is repeated.
In other words, the ball starts from a height, touches the floor at height 0, and then returns to the player's hand repeatedly.
This means that the graph will have an up and down motion and therefore the graph in answer (b) is correct.
Is the function in the graph decreasing?
Because the basketball hits the ground between each bounce! When the ball touches the floor, its height is exactly zero, so the graph must cross the x-axis at these points.
In real life, yes! Each bounce loses energy due to friction and air resistance. But for this problem, we focus on the basic pattern - regular up and down motion touching the ground.
A straight line would mean the ball is constantly rising at the same rate. But bouncing involves falling down and rising up repeatedly, creating wave-like motion.
Look for these clues:
Then you'd see a horizontal line at constant height! The key word 'bounces' tells us the ball moves up and down repeatedly.
Get unlimited access to all 18 Functions questions, detailed video solutions, and personalized progress tracking.
Unlimited Video Solutions
Step-by-step explanations for every problem
Progress Analytics
Track your mastery across all topics
Ad-Free Learning
Focus on math without distractions
No credit card required • Cancel anytime