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A1-F-2-2

Page history last edited by Brenda Butz 6 years, 3 months ago

A1.F.2.2 Recognize the graph of the functions f(x)=x and f(x)=|x| and predict the effects of transformations [f(x+c)and f(x)+c, where c is a positive or negative constant] algebraically and graphically using various methods and tools that may include graphing calculators.

In a Nutshell

Students will recognize the parent graphs of a linear and absolute value function and use various methods,including graphing calculators, to investigate vertical and horizontal transformations

Student Actions	Teacher Actions
Students discover vertical and horizontal translations and develop a deep and flexible conceptual understanding about how they affect a graph and its table of values in a variety of functions. Students explore graphs and tables of the parent functions f(x) =x and f(x) = \|x\| , and apply transformations to discover the horizontal and vertical transformations. Students will develop the ability to communicate mathematically when given g(x) = f(x) +c where students will explain the similarities and differences between f(x) and g(x)	Facilitate meaningful mathematical discourse by providing students with opportunities to compare and contrast graphs of the parent functions and the transformed graphs. Pose purposeful questions by creating examples and asking questions that focus on noticing the effect of a translation. “What do you notice about the difference between f(x) =x, g(x)=x+3 and m(x) = (x+3)? What do you predict will happen to the graphs of these equations?” “Did your prediction happen?” “Why did g(x) move vertically while m(x) moved horizontally?” “Can you create a function that moves both horizontally and vertically?”
Key Understandings	Misconceptions
Translations of the parent function of linear or absolute value can be represented graphically and within the equation. The use of graphing utilities can help students visualize the changes that various translations make in the graph of a function.	Students may move translations in the opposite direction. Example: f(x)=(x+3) is a translation of 3 units to the right rather than to the left. Students may interchange the horizontal and vertical translations.