Activity
In a bungee jump, the height of the jumper is a function of time since the jump begins.
Expressions and Equations:
Features:
- first dip in the graph
- vertical intercept
- first peak in the graph
- horizontal intercept
- maximum
1. Match each description about the jump to a corresponding expression or equation and to a feature on the graph.
One expression or equation does not have a matching verbal description. Its corresponding graphical feature is also not shown on the graph. Interpret that expression or equation in terms of the jump and in terms of the graph of the function. Record your interpretation in the last row of the table.
Description of Jump |
Expression or Equation |
Feature of Graph |
A. the greatest height that the jumper is from the river |
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B. the height from which the jumper was jumping |
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C. the time at which the jumper reached the highest point after the first bounce |
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D. the lowest point that the jumper reached in the entire jump |
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E. the time at which the jumper hits the surface of the river |
A.Expression or Equation
Compare your answer:
Feature of Graph
Compare your answer:
maximum
B. Expression or Equation
Compare your answer:
Feature of Graph
Compare your answer:
vertical intercept
C. Expression or Equation
Compare your answer:
Feature of Graph
Compare your answer:
first peak in the graph
D. Expression or Equation
Compare your answer:
Feature of Graph
Compare your answer:
first dip in the graph; also the minimum of the graph shown
E. Description of Jump
Compare your answer:
the time at which the jumper hits the surface of the river
Expression or Equation
Compare your answer:
Feature of Graph
Compare your answer:
horizontal intercept
2. Use the graph to:
A. estimate and .
Compare your answers:
is 80, and is about 10.
2. If , then equals what value?
Compare your answer:
3. If , then equals what value?
Compare your answer:
The approximate solutions to are and .
4. If , then equals what value?
Compare your answer:
There is no solution to when is between 0 and 35, which is what is shown on the graph. We don't know if the function will have a solution when is greater than 35.
Video: The Meaning of Function Notation
Watch the following video to learn more about connecting graphical and verbal representations of a function.
The horizontal intercept is also called the -intercept, or zero .
The vertical intercept is also called the -intercept.
Are you ready for more?
Extending Your Thinking
Based on the information available, how long do you think the bungee cord is? Make an estimate and explain your reasoning.
Compare your answers:
About 50 meters. The low points on the graph increase with each bounce, and the high points decrease. They look like they are approaching about 30 meters in height above the river. Since the jump started from 80 meters above the river, this means that the bungee cord is about 50 meters long.
Self Check
Additional Resources
More Real-Life Graphs
The graph below represents the total number of smartphones that are shipped to a retail store over the course of 50 days.
Why does ?
Since section B is not changing, it represents the period of time where the store did not receive new shipments, so .
Try it
Try It: More Real-Life Graphs
The relationship between Jameson’s account balance , in dollars, and time , in days, is modeled by the graph below.
What does the point represent in the context of the problem?
Here is how to describe what represents in the context of the problem:
represents the maximum amount of money Jameson had in his account over the time period shown. It also represents that after 9 days, Jameson had $98 in his account. It is the maximum because it is the highest point on the graph provided.