Module 3: Linear and exponential functions

Topic A: Lessons 1-3: Arithmetic sequence intro

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Sequences intro
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Intro to arithmetic sequences
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Intro to arithmetic sequences
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Extending arithmetic sequences
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Using arithmetic sequences formulas
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Intro to arithmetic sequence formulas
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Worked example: using recursive formula for arithmetic sequence
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Practice

Extend arithmetic sequencesGet 3 of 4 questions to level up!
Use arithmetic sequence formulasGet 5 of 7 questions to level up!

Topic A: Lessons 1-3: Geometric sequence intro

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Intro to geometric sequences
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Extending geometric sequences
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Using explicit formulas of geometric sequences
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Using recursive formulas of geometric sequences
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Practice

Extend geometric sequencesGet 3 of 4 questions to level up!
Extend geometric sequences: negatives & fractionsGet 4 of 5 questions to level up!
Use geometric sequence formulasGet 3 of 4 questions to level up!

Topic A: Lessons 1-3: Arithmetic sequence formulas

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Explicit formulas for arithmetic sequences
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Explicit formulas for arithmetic sequences
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Arithmetic sequence problem
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Recursive formulas for arithmetic sequences
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Recursive formulas for arithmetic sequences
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Converting recursive & explicit forms of arithmetic sequences
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Converting recursive & explicit forms of arithmetic sequences
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Practice

Explicit formulas for arithmetic sequencesGet 3 of 4 questions to level up!
Recursive formulas for arithmetic sequencesGet 3 of 4 questions to level up!
Converting recursive & explicit forms of arithmetic sequencesGet 3 of 4 questions to level up!

Topic A: Lessons 1-3: Geometric sequence formulas

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Explicit & recursive formulas for geometric sequences
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Converting recursive & explicit forms of geometric sequences
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Sequences word problems
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Practice

Explicit formulas for geometric sequencesGet 3 of 4 questions to level up!
Recursive formulas for geometric sequencesGet 3 of 4 questions to level up!
Converting recursive & explicit forms of geometric sequencesGet 3 of 4 questions to level up!
Sequences word problemsGet 3 of 4 questions to level up!

Topic A: Lessons 4-6: Exponential growth

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Intro to exponential functions
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Exponential vs. linear growth
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Exponential vs. linear models: verbal
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Exponential vs. linear models: table
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Exponential expressions word problems (numerical)
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Initial value & common ratio of exponential functions
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Exponential expressions word problems (algebraic)
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Interpreting exponential expression word problem
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Practice

Warmup: exponential vs. linear growthGet 3 of 3 questions to level up!
Exponential vs. linear growthGet 3 of 4 questions to level up!
Exponential vs. linear modelsGet 3 of 4 questions to level up!
Exponential expressions word problems (numerical)Get 3 of 3 questions to level up!
Exponential expressions word problems (algebraic)Get 3 of 4 questions to level up!
Interpret exponential expressions word problemsGet 3 of 4 questions to level up!

Topic A: Lesson 7: Exponential decay

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Exponential function graph
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Graphs of exponential growth
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Exponential decay intro
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Graphing exponential growth & decay
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Exponential growth & decay word problems
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Practice

Graphs of exponential growthGet 3 of 4 questions to level up!
Exponential growth vs. decayGet 3 of 4 questions to level up!
Graphing exponential growth & decayGet 3 of 4 questions to level up!

Topic B: Lessons 8-12: Functions intro

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Lesson 8: No content yet
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What is a function?
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Worked example: Evaluating functions from equation
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Worked example: Evaluating functions from graph
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Worked example: evaluating expressions with function notation
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Practice

Evaluate functionsGet 3 of 4 questions to level up!
Evaluate functions from their graphGet 3 of 4 questions to level up!
Evaluate function expressionsGet 3 of 4 questions to level up!

Topic B: Lessons 8-12: Function domain and range

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What is the domain of a function?
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What is the range of a function?
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Intervals and interval notation
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Worked example: domain and range from graph
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Domain of a radical function
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Worked example: domain of algebraic functions
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Practice

Domain and range from graphGet 5 of 7 questions to level up!
Determine the domain of functionsGet 3 of 4 questions to level up!

Topic B: Lessons 8-12: Recognizing functions

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Recognizing functions from graph
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Does a vertical line represent a function?
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Recognizing functions from table
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Recognizing functions from verbal description
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Recognizing functions from verbal description word problem
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Practice

Recognize functions from graphsGet 3 of 4 questions to level up!
Recognize functions from tablesGet 3 of 4 questions to level up!

Topic B: Lesson 13: Interpreting the graph of a function

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Increasing, decreasing, positive or negative intervals
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Worked example: positive & negative intervals
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Introduction to minimum and maximum points
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Worked example: absolute and relative extrema
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Graph interpretation word problem: temperature
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Graph interpretation word problem: basketball
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Practice

Positive and negative intervalsGet 3 of 4 questions to level up!
Increasing and decreasing intervalsGet 3 of 4 questions to level up!
Relative maxima and minimaGet 3 of 4 questions to level up!
Absolute maxima and minimaGet 3 of 4 questions to level up!
Graph interpretation word problemsGet 3 of 4 questions to level up!

Topic B: Lesson 14: Linear and exponential Models—comparing growth rates

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Exponential vs. linear growth over time
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Practice

Exponential vs. linear growth over timeGet 3 of 4 questions to level up!

Topic C: Lesson 15: Piecewise functions

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Introduction to piecewise functions
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Worked example: evaluating piecewise functions
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Worked example: graphing piecewise functions
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Worked example: domain & range of step function
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Worked example: domain & range of piecewise linear functions
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Practice

Evaluate piecewise functionsGet 3 of 4 questions to level up!
Evaluate step functionsGet 3 of 4 questions to level up!
Piecewise functions graphsGet 3 of 4 questions to level up!

Topic C: Lessons 16-20: Graphing absolute value functions

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Lesson 16: No content yet
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Shifting absolute value graphs
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Scaling & reflecting absolute value functions: equation
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Scaling & reflecting absolute value functions: graph
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Graphing absolute value functions
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Practice

Shift absolute value graphsGet 3 of 4 questions to level up!
Scale & reflect absolute value graphsGet 3 of 4 questions to level up!
Graph absolute value functionsGet 3 of 4 questions to level up!

Topic D: Using functions and graphs to solve problems

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Topic D: No content yet
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About this unit

"In earlier grades, students define, evaluate, and compare functions and use them to model relationships between quantities. In this module, students extend their study of functions to include function notation and the concepts of domain and range. They explore many examples of functions and their graphs, focusing on the contrast between linear and exponential functions. They interpret functions given graphically, numerically, symbolically, and verbally; translate between representations; and understand the limitations of various representations." Eureka Math/EngageNY (c) 2015 GreatMinds.org