Common Core Standards: Math
2. 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.
Jon's grandmother moved to the U.S. from Italy when she was in her twenties. Over the years, she's done a great job of learning English, but every once in a while she says something that's a little off. For instance, during a production of Into the Woods, she wished him a spirited, "In the mouth of the wolf!" It meant something very different to her than it did to Jon, who played one of the three little pigs.
Functions are kind of like Jon's grandmother and her language situation. Some ideas translate well from one interpretation to another. Other ideas simply don't.
Students should know that there are a number of ways of expressing the idea of a function. A word problem, a graph, a table of values, and an algebraic equation can all be used to express the same idea. Translating these ideas from one form to another will be useful especially when two different representations of functions have to be compared.
In order to convert functions from word problems to tables, equations, and graphs, students need to know what functions are and how to handle them. Thankfully, little mistakes in translation can be easily checked if students remember the definition of a function and use their knowledge of linear equations. When it comes to Jon and his nonna, though, he may just need to brush up on his Italian skills.