options: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in Grade 8.)

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
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