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A2-F-1-1

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

A2.F.1.1 Use algebraic, interval, and set notations to specify the domain and range of functions of various types and evaluate a function at a given point in its domain.


In a Nutshell

There are various ways to express the domain and range of a function. Students will use algebraic, interval and set notations to identify the domain and range of a function.

Student Actions

Teacher Actions

  • Students will communicate mathematically through discussion, writing, reading, interpreting and translating the domain and range of any function or graph to algebraic, interval and/or set notation.

  • Students will develop accurate and appropriate procedural fluency as they learn efficient procedures to find the correct range value of a function given its domain value algebraically or graphically. 

 

  • Pose purposeful questions allowing students to identify and use different notations for domain and range of a function.

  • Help students show evidence of their thinking and conceptual understanding by implementing tasks that allow them to use, discuss, and make connections among the various notations for domain and range of a function.

  • Implement tasks with differentiated opportunities to evaluate a function algebraically or graphically at a given point in its domain.

  • Facilitate meaningful mathematical discourse as students engage with graphs and function equations to determine the domain and range.

  • Support productive struggle as students discuss and justify domain and range intervals for various functions and graphs.

Key Understandings

Misconceptions

  • When interpreting domain and range graphically or algebraically, write the domain and range from least to greatest. 

  • Write breaks in the domain or range, using more than one interval when written in interval notation or more than one inequality when written in algebraic or set notation.

  • Realize set notation is similar to algebraic notation with {xl }.

  • In interval notation, use the brackets in place of > or < and parentheses are used in place of < or >.

  • Graphically, f(x)=y; therefore, evaluate a function at a given point in its domain by locating the y-coordinate that corresponds to the given x-coordinate
  • Replace every x in the function with the given domain value and simplify the expression when evaluating f(x) algebraically.

Procedural:

  • Students do not write the domain from low to high when using interval notation.

  • Students have difficulty interpreting the symbols of set notation.

  • Students do not know when to use brackets or parentheses in interval notation.

Conceptual:

  • Students incorrectly combine two disjoint sets into one inequality.

  • Students have difficulty finding the range or domain of a function from its graph.

  • Students have difficulty finding the domain and range of a piecewise function graphically.

  • Students are confused which function piece to evaluate when evaluating a piecewise function at a given point.

  • Students have difficulty evaluating a function at a given point in its domain.

OKMath Framework Introduction

Algebra 2 Grade Introduction

 

 

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