options: Build a function that models a relationship between two quantities.

Define, evaluate, and compare functions.

Construct and compare linear and exponential models and solve problems.

Build new functions from existing functions.

Prove and apply trigonometric identities.

Extend the domain of trigonometric functions using the unit circle.

Understand the concept of a function and use function notation.

Model periodic phenomena with trigonometric functions.

Interpret functions that arise in applications in terms of the context.

Interpret expressions for functions in terms of the situation they model.

Use functions to model relationships between quantities.

Analyze functions using different representations.
problem_activity: Task
A function machine takes an input, and based on some rule produces an output.
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The tables below show some input-output pairs for different functions. For each table, describe a function rule in words that would produce the given outputs from the corresponding inputs. Then fill in the rest of the table values as inputs and outputs which are consistent with that rule.
Input values can be any English word. Output values are letters from the English alphabet.
$\ \ \ \ \ $
{"table": [{"_attributes": {"class": ["regular"]}, "tbody": [{"tr": [{"th": [{"_value": "input"}], "td": [{"_value": "cat"}, {"_value": "house"}, {"_value": "you"}, {"_value": "stem"}, {"_value": "$\\ \\ \\ \\ \\ $"}, {"_value": "$\\ \\ \\ \\ \\ $"}, {"_value": "$\\ \\ \\ \\ \\ $"}]}, {"th": [{"_value": "output"}], "td": [{"_value": "t"}, {"_value": "e"}, {"_value": "u"}, {}, {"_value": "z"}, {}, {}]}]}]}]}
Input values can be any rational number. Output values can be any rational number.
{"table": [{"_attributes": {"class": ["regular"]}, "tbody": [{"tr": [{"th": [{"_value": "input"}], "td": [{"_value": "$2$"}, {"_value": "$5$"}, {"_value": "$-1.53$"}, {"_value": "$0$"}, {"_value": "$-4 $"}, {"_value": "$\\ \\ \\ \\ \\ $"}, {"_value": "$\\ \\ \\ \\ \\ $"}]}, {"th": [{"_value": "output"}], "td": [{"_value": "$7$"}, {"_value": "$10$"}, {"_value": "$3.47$"}, {"_value": "$5$"}, {}, {"_value": "$8$"}, {}]}]}]}]}
Input values can be any whole number. Output values can be any whole number.
{"table": [{"_attributes": {"class": ["regular"]}, "tbody": [{"tr": [{"th": [{"_value": "input"}], "td": [{"_value": "$1$"}, {"_value": "$2$"}, {"_value": "$3$"}, {"_value": "$4$"}, {"_value": "$5$"}, {"_value": "$6$"}, {"_value": "$7$"}]}, {"th": [{"_value": "output"}], "td": [{"_value": "$2$"}, {"_value": "$1$"}, {"_value": "$4$"}, {"_value": "$\\ \\ \\ \\ \\ $"}, {}, {}, {}]}]}]}]}
Input values can be any whole number between 1 and 365. Output values can be any month of the year.
{"table": [{"_attributes": {"class": ["regular"]}, "tbody": [{"tr": [{"th": [{"_value": "input"}], "td": [{"_value": "25"}, {"_value": "365"}, {"_value": "35"}, {"_value": "95"}, {"_value": "330"}, {"_value": "66"}, {}]}, {"th": [{"_value": "output"}], "td": [{"_value": "January"}, {"_value": "December"}, {"_value": "February"}, {"_value": "April"}, {"_value": "November"}, {"_value": "$\\ \\ \\ \\ \\ \\ \\ \\ $"}, {"_value": "October"}]}]}]}]}
For at least one of the tables, describe a second rule which fits the given pairs but ultimately produces different pairs than the first rule for the rest of the table.


correct_option_index: 1