A1-F-2-2


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.

OKMath Framework Introduction

Algebra 1 Introduction