What Is A Function



Activity 8.3 Combinations of Functions

Overview:

Students are given a table of values of braking distance and reaction distance for several speeds and asked to create a scatter plots of speed vs. braking and reaction distances. They are then asked to create a scatter plot of speed vs. total distance, which is the sum of braking and reaction distances, and to find the function that represents total distance.

Estimated Time Required:

The activity should take approximately 30 minutes.

Technology: None

Concepts:

• Creating and interpreting new functions by arithmetically combining given functions

Discussion:

This activity illustrates a real-world application of combinations of functions.

Activity 8.3 Combinations of Functions

The following table was compiled by Michael J. Shepston & Associates and contains data for stopping distances at various speeds. This information is based on full braking, on dry, level asphalt, with an average perception-reaction time of 1.5 seconds. Distances given were measured in feet. Complete the table for Total Distance.

|Speed |Braking |Reaction |Total |

|in MPH |Distance |Distance |Distance |

|10 |5 |22 | |

|15 |11 |33 | |

|20 |19 |44 | |

|25 |30 |55 | |

|30 |43 |66 | |

|35 |59 |77 | |

|40 |76 |88 | |

|45 |97 |99 | |

|50 |119 |110 | |

1. Make a scatter plot of Speed vs. Braking Distance.

[pic]

2. Find a function for the Braking Distance, B(x) that fits the data and graph it on the scatter plot above.

B(x) =

3. Make a scatter plot of Speed vs. Reaction Distance.

[pic]

4. Find a function for the Reaction Distance, R(x) that fits the data and graph it on the scatter plot above.

R(x) =

5. Make a scatter plot of Speed vs. Total Distance.

[pic]

6. Find the new function (B + R)(x) and graph it on the scatter plot above.

(B + R)(x) =

7. Does this new function fit the Speed vs. Total Distance data? Why or why not?

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