**Name** |
**Description** |

A Sum of Functions | In this example, students are given the graph of two functions and are asked to sketch the graph of the function that is their sum. The intent is that students develop a conceptual understanding of function addition. |

Basic Linear Function | This video demonstrates writing a function that represents a real-life scenario. |

Compounding with a 100% Interest Rate | This task provides an approximation, and definition, of *e*, in the context of more and more frequent compounding of interest in a bank account. The approach is computational. |

Compounding with a 5% Interest Rate | This task develops reasoning behind the general formula for balances under continuously compounded interest. While this task itself specifically address the standard (F-BF), building functions from a context, an auxiliary purpose is to introduce and motivate the number *e*, which plays a significant role in the (F-LE) domain of tasks. |

Crude Oil and Gas Mileage | This task asks students to write expressions for various problems involving distance per units of volume. |

Data Flyer | Using this virtual manipulative, students are able to graph a function and a set of ordered pairs on the same coordinate plane. The constants, coefficients, and exponents can be adjusted using slider bars, so the student can explore the affect on the graph as the function parameters are changed. Students can also examine the deviation of the data from the function. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet. |

Flu on Campus | The context of this example is the spread of a flu virus on campus and the related sale of tissue boxes sold. Students interpret the composite function and determine values simply by using the tables of values. |

Graphs of Compositions | This task addresses an important issue about inverse functions. In this case the function *f* is the inverse of the function *g* but *g* is not the inverse of *f* unless the domain of *f* is restricted. |

Lake Algae | The purpose of this task is to introduce students to exponential growth. While the context presents a classic example of exponential growth, it approaches it from a non-standard point of view. |

Number Cruncher | In this activity, students enter inputs into a function machine. Then, by examining the outputs, they must determine what function the machine is performing. This activity allows students to explore functions and what inputs are most useful for determining the function rule. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet. |

Skeleton Tower | This problem is a quadratic function example. The other tasks in this set illustrate MAFS.912.F.BF.1.1.a in the context of linear, exponential, and rational functions. |

Summer Intern | This task asks students to use proportions of mass and volume to create ideal brine for saltwater fish tanks. It also asks students to compare graphs. |

Susita's Account | This task asks students to determine a recursive process from a context. Students who study computer programming will make regular use of recursive processes. |

Temperature Conversions | Unit conversion problems provide a rich source of examples both for composition of functions (when several successive conversions are required) and inverses (units can always be converted in either of two directions). |

The Canoe Trip, Variation 1 | The purpose of this task is to give students practice constructing functions that represent a quantity of interest in a context, and then interpreting features of the function in the light of the context. It can be used as either an assessment or a teaching task. |

The Canoe Trip, Variation 2 | The primary purpose of this task is to lead students to a numerical and graphical understanding of the behavior of a rational function near a vertical asymptote, in terms of the expression defining the function. |