• If you are citizen of an European Union member nation, you may not use this service unless you are at least 16 years old.

• Work with all your cloud files (Drive, Dropbox, and Slack and Gmail attachments) and documents (Google Docs, Sheets, and Notion) in one place. Try Dokkio (from the makers of PBworks) for free. Now available on the web, Mac, Windows, and as a Chrome extension!

View

# A1-F-2-2

last edited by 3 years, 9 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 