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# A1-F-2-2

last edited by 6 years, 7 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

## 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?”

## 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.

OKMath Framework Introduction

Algebra 1 Introduction