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Algebra 1

4.6.3 Connecting Graphical and Verbal Representations of a Function

Algebra 14.6.3 Connecting Graphical and Verbal Representations of a Function

4.6.3 Connecting Graphical and Verbal Representations of a Function

4.6.3 • Connecting Graphical and Verbal Representations of a Function

Activity

In a bungee jump, the height of the jumper is a function of time since the jump begins.

Expressions and Equations:

  • h ( 0 ) h ( 0 )
  • h ( t ) = 0 h ( t ) = 0
  • h ( 4 ) h ( 4 )
  • h ( t ) = 80 h ( t ) = 80
  • h ( t ) = 45 h ( t ) = 45

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.

A.Expression or Equation

Feature of Graph

B. Expression or Equation

Feature of Graph

C. Expression or Equation

Feature of Graph

D. Expression or Equation

Feature of Graph

E. Description of Jump

Expression or Equation

Feature of Graph

2. Use the graph to:

A. estimate h ( 0 ) h ( 0 ) and h ( 4 ) h ( 4 ) .

2. If t = 4 t = 4 , then h ( 4 ) h ( 4 ) equals what value?

3. If h ( t ) = 45 h ( t ) = 45 , then t t equals what value?

4. If h ( t ) = 0 h ( t ) = 0 , then t t equals what value?

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.

Video: The Meaning of Function Notation

Watch the following video to learn more about connecting graphical and verbal representations of a function.

The Meaning of Function Notation

The horizontal intercept is also called the x x -intercept, or zero .

The vertical intercept is also called the y y -intercept.

Self Check

The graph models the height, in feet, of a kickball over time. When is the ball at its maximum height?


  1. h ( 2.5 ) = 31 ; The maximum height is about 2.5 feet. It occurred about 31 seconds after the ball was kicked.
  2. h ( 1 ) = 20 ; The maximum height occurred 1 second after the ball was kicked.
  3. h ( 5 ) = 0 ; The maximum height occurs about 6 seconds after the ball was kicked.
  4. h ( 2.5 ) = 31 ; The maximum height is about 31 feet. It occurred about 2.5 seconds after the ball was kicked.

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 f ( 20 ) = f ( 22 ) f ( 20 ) = f ( 22 ) ?

Since section B is not changing, it represents the period of time where the store did not receive new shipments, so f ( 20 ) = f ( 22 ) f ( 20 ) = f ( 22 ) .

Try it

More Real-Life Graphs

The relationship between Jameson’s account balance B B , in dollars, and time t t , in days, is modeled by the graph below.

What does the point B ( 9 ) = 98 B ( 9 ) = 98 represent in the context of the problem?

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