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A2-F-1-4

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

A2.F.1.4 Graph exponential and logarithmic functions. Identify asymptotes and x- and y-intercepts using various methods and tools that may include graphing calculators or other appropriate technology. Recognize exponential decay and growth graphically and algebraically.


In a Nutshell

Students will graph, identify critical points and analyze logarithmic, exponential growth and exponential decay functions. This can be accomplished through various methods and tools to include technology.

Student Actions

Teacher Actions

  • Students will develop a deep and flexible conceptual understanding of asymptotes as a line that the graph of a function approaches but never crosses.

  • Students will develop a deep and flexible conceptual understanding of the parent functions of exponential and logarithmic functions. Students will be able to generalize the changes in the graphs of the parent functions of exponential and logarithmic functions using properties of transformations.

  • Students will use various means to develop a deep conceptual understanding of asymptotes and x- and y intercepts as related to exponential and logarithmic functions. (ie desmos, graphing calculators, tables, equations, etc.)

  • Students will discuss and describe the behavior of the graphs of exponential and logarithmic functions, noting the intercepts and asymptotes. Students will justify their reasoning verbally and in writing.

  • Students will make conjectures about an asymptote given a graph based on the repeated structures in the graphs of exponential and logarithmic functions.

  • Students will learn develop accurate and appropriate procedural fluency for finding asymptotes of exponential and logarithmic functions. These procedures could include the use various methods and tools.

  • Students will develop a deep and flexible conceptual understanding of the difference between exponential growth and decay.
  • Pose purposeful questions that will assess and advance student understanding of asymptotes by asking questions that build on, but do not take over or funnel, student thinking.

  • Provide activities and allow time for students to investigate, ponder and grapple with the graphs of exponential and logarithmic functions.

  • Use visual models to support student understanding of the location of an asymptote on a graph.

  • Anticipate what students might struggle with when finding asymptotes of exponential and logarithmic functions and be prepared to support them productively through the struggle.

  • Facilitate meaningful mathematical discourse by developing situations to allow students to discover the differences between exponential growth and decay functions both graphically and algebraically. (Investigation with desmos, graphing calculator, a table, multiple graphs, etc.) Allow students to discuss their findings.

  • Elicit and use evidence of student thinking by providing real world problems and allowing students to investigate exponential growth and decay functions. Allow students to represent their conjectures and generalizations in a variety of ways (their choice).

 

Key Understandings

Misconceptions

  • Graph exponential and logarithmic functions.

  • Recognize the parent functions of exponential and logarithmic functions and apply transformations to these each.

  • Identify asymptotes and describe the behavior of the graph as it approaches the asymptote.

  • Exponential graphs have horizontal asymptotes and logarithms have vertical asymptotes.

  • Recognize exponential growth and decay graphically and algebraically.

  • Students incorrectly write asymptotes and intercepts as a single integer.

  • Students don’t understand that exponential and logarithmic graphs will never cross their asymptotes.

  • Students have difficulty learning the parent graph for exponential and logarithmic functions.

  • Students struggle with determining an algebraic representation of a exponential growth vs. decay.

  • Students do not see the connection between the growth and decay function and the their graphs.

 

OKMath Framework Introduction

Algebra 2 Grade Introduction

 

 

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