Activity
A tennis ball was dropped from a certain height. It bounced several times, rolled along for a short period, and then stopped. Function gives its height over time.
Here is a partial graph of . Height is measured in feet. Time is measured in seconds.
Use the graph to help you answer the questions.
Be prepared to explain what each value or set of values means in this situation.
1. Find . What point is this on the graph? What does it represent?
Compare your answer:
. It tells us the ball was dropped from a height of 6 feet at .
2. Solve .
Compare your answer:
, , and are three possible solutions, but there are others. Each one represents the time when the ball hit the ground.
3. Describe the domain of the function.
Compare your answer:
The domain includes all values between 0 and the time when the ball stopped moving, which, based on the graph, is about 3.8.
4. Describe the range of the function.
Compare your answer:
The range includes all values between 0 and 6 feet, the height from which the ball was dropped.
Video: Interpreting Function Notation
Watch the following video to learn more about function notation.
Are you ready for more?
Extending Your Thinking
In function , the input was time in seconds, and the output was height in feet.
Think about some other quantities that could be inputs or outputs in this situation.
1. Describe a function whose domain includes only integers. Be sure to specify the units.
Compare your answer:
The maximum height, in feet, that the ball reaches after bounces as a function of the number of bounces.
2. Sketch a graph of this function.
Compare your answer:
3. Describe a function whose range includes only integers. Be sure to specify the units.
Compare your answer:
The number of times the ball has hit the ground as a function of time, in seconds, since the ball was dropped.
4. Sketch a graph of this function.
Compare your answer:
Self Check
Additional Resources
Domain and Range from Graphs
The graph below shows the distance Carl drives from home, , when is time in seconds.
What is the domain of the graph?
The domain is -values that are at least 0 and a maximum of 400.
What is the range of the graph?
The range is the -values that are at least 0 and a maximum of 285.
What are the values of where , and what do they mean?
and , and this is when Carl left home and then arrived home, so the distance was 0.
Try it
Try It: Domain and Range from Graphs
What are the values for the domain and range of the graph below?
Here is how to find the domain and range of the graph:
The domain includes the -values or inputs of the graph. The domain is from at least 0 to at most 10.
The range includes the -values or outputs of the graph. The range is from at least 1 to at most 3.