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A2-F-1-2

Page history last edited by Tashe Harris 6 years, 1 month ago

A2.F.1.2 Recognize the graphs of exponential, radical (square root and cube root only), quadratic, and logarithmic functions. Predict the effects of transformations [f(x+c),f(x)+c,  f(cx) and cf(x) where c is a positive or negative real-valued constant] algebraically and graphically, using various methods and tools that may include graphing calculators or other appropriate technology.


In a Nutshell

Beginning with a function, students will identify how to translate, reflect, rotate and dilate the graph to produce a new function, both algebraically and graphically.

Student Actions

Teacher Actions

  • Students will develop a productive mathematical disposition as they work through composition of transformations on parent functions.

  • Students will make and test conjectures using various tools about the transformations of functions and extending to the composition of transformations of functions..

  • Students will make predictions, conjectures and generalizations regarding each transformation within a function and its effect on the parent function.

  • Students will identify parent functions of a graph by generalizing visual patterns and characteristics of transformations.

  • Students will develop procedural fluency through practice of the application of transformation of functions.

  • Students will communicate mathematically by explaining and justifying the effects of transformations on a graph of a function.

  • Facilitate meaningful mathematical discourse by providing tasks that allow students to predict the effects of transformations and then verify their predictions through writing and verbal discussion with the aid of various tools which may include technology. (ie desmos, graphing calculator)

  • Elicit and use evidence of student thinking as they discuss and defend their predictions on the effects of transformations to a parent function.

  • Pose purposeful questions asking students to match equations with the graph of the parent function and support productive struggle as students grapple with multiple ways to achieve given transformations..

  • Support productive struggle in learning mathematics by providing  students with the opportunity to apply transformation to graphs of functions that model real world situations.

 

Key Understandings

Misconceptions

  • Identify the parent function in equation or graph form.

  • Understand vertical translations of a function f(x) + c, means moving up if c > 0 and down if c < 0.

  • Understand horizontal translation of a function, f(x + c), means moving left if c > 0 and right if c < 0.

  • Understand vertical stretch of a function, cf(x), when c > 0 and a compression when 0 < c < 1.

  • Understand f(cx) is a horizontal stretch of a function when c >0 and a compression when 0<c<1.
  • Understand cf(x) is a reflection of a function when c<0.

  • Students confuse f( x + c) with f(x) +c moving in the wrong direction.
  • When c > 1, students interpret f(cx) as a horizontal stretch, and when 0 < c < 1, students interpret f(cx) as a horizontal compression.
  • Students misinterpret a negative leading coefficient in a function.
  • Students have a hard time identifying the parent function.

OKMath Framework Introduction

Algebra 2 Grade Introduction

 

 

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