ALEX Classroom Resource

  

Linearization of a Function

  Classroom Resource Information  

Title:

 Linearization of a Function

URL:

 https://www.ck12.org/c/calculus/tangent-line-approximation/lesson/Linearization-of-a-Function-CALC/?referrer=concept_details

Content Source:

 Other
CK-12
Type: Informational Material

Overview:

Suppose you absolutely needed to know the value of the square root of 19 but all you had was pencil and paper, no calculator. Could you calculate it? With your current understanding of the derivative as the slope of a tangent line, you should be able to. Try computing √19 without a calculator; then compare your result with this concept's method of linearization and a calculator.

This informational material will explain how to create a linear representation of non-linear data, using technology and by-hand calculations. There is a corresponding video available. Practice questions with a PDF answer key are provided.  

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 9-12
Mathematical Modeling
16. Create a linear representation of non-linear data and interpret solutions, using technology and the process of linearization with logarithms.

Unpacked Content
Evidence Of Student Attainment:
Students:
  • Can use logarithmic properties to create a linear representation of non-linear data.
Teacher Vocabulary:
  • Non-linear
  • Linearization
Knowledge:
Students know:
  • the properties of logarithms and can use them to rewrite problems in different forms.
Skills:
Students are able to:
  • use the power property of logarithms.
  • Recognize the difference between a linear and a nonlinear function.
Understanding:
Students understand:
  • It is often easier to solve linear functions rather than non-linear functions.
  • The use of logarithmic properties allows you to rewrite exponential functions as linear functions.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
MMOD.16.1: Define linearization, linear, non-linear, exponential function and logarithmic function.
MMOD.16.2: Interpret solutions based on results.
MMOD.16.3: Using technology create a linear representation of nonlinear data.
MMOD.16.4: Using technology graph a logarithmic function.
MMOD.16.5: Using technology graph an exponential function.

Prior Knowledge Skills:
  • Define logarithmic and exponential function.
  • Recognize the inverse relationship of logarithmic function and exponential functions.
  • Define ordered pair, coordinate plane, polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions.
  • Create equations with two variables (polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions).
  • Graph equations on coordinate axes with labels and scales (polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions.).
  • Define linear function and exponential function.
  • Distinguish between graphs of a line and an exponential function.
  • Identify the graph of an exponential function.
Tags: data, linear, linearization, mathematical modeling, nonlinear, representation, square root
License Type: Custom Permission Type
See Terms: https://www.ck12info.org/terms-of-use/
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses
AccessibilityText Resources: Content is organized under headings and subheadings
Video resources: includes closed captioning or subtitles
Comments
  This resource provided by:  
Author: Hannah Bradley
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