Algebra 2 (& GT)
Unit 5: Exponential and Logarithmic Functions
What will my child learn?
Students will:
Understand the concept of a function and use function notation.
F.IF.A.3
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers (SAT® Content  PAM.14).
Build a function that models a relationship between two quantities.
F.BF.A.2
Write geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
Construct and compare linear and exponential models and solve problems.
F.LE.A.2
Construct exponential functions, including geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table) (SAT® Content  PAM.01).
Interpret expressions for functions in terms of the situations they model.
F.LE.B.5
Interpret the parameters in an exponential function in terms of a context (SAT® Content  PAM.12).
Write expressions in equivalent forms to solve problems.
A.SSE.B.4
Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.
Build new functions from existing functions.
F.BF.B.4
Find inverse functions. Focus on linear functions, but consider simple situations where the domain of the function must be restricted in order for the inverse to exist, such as f(x) = x^2, x > 0.
a. Solve an equation of the form f(x) = c. For example, f(x) = 2x^3 or f(x) = (x + 1)/(x – 1) for x ≠ 1.
Analyze functions using different representations.
F.IF.C.7
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*
e. Graph exponential and logarithmic functions, showing intercepts and end behavior.
Interpret functions that arise in applications in terms of a context.
F.IF.B.4
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*
Interpret linear and exponential functions that arise in applications in terms of a context.
F.IF.B.6
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Analyze functions using different representations.
F.IF.C.9
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
Build a function that models a relationship between two quantities.
F.BF.A.1
Write a function that describes a relationship between two quantities.*
b. Combine standard function types using arithmetic operations.
Write expressions in equivalent forms to solve problems
A.SSE.B.3
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
c. Use the properties of exponents to transform expressions for exponential functions.
Build new functions from existing functions.
F.BF.B.3
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
Represent and solve equations graphically.
A.REI.D.11
Explain why the xcoordinates of the points where the graphs of the equations y=f(x) and y=g(x) intersect are the solutions of the equation f(x)=g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, exponential, and logarithmic functions.*
Construct and compare linear, quadratic, and exponential models and solve problems.
F.LE.A.4
For exponential models, express as a logarithm the solution to a b^ct = d, where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.
Students will:
Understand the concept of a function and use function notation.
F.IF.A.3
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers (SAT® Content  PAM.14).
 Check for Understanding: Defining Sequences as Functions  Modeling with Sequences
 Review/Rewind: Intro to Sequences
 Enrichment Tasks: Snake on a Plane
Build a function that models a relationship between two quantities.
F.BF.A.2
Write geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
 Check for Understanding: Modeling with Sequences
 Review/Rewind: What Is a Geometric Sequence?  Sequences Word Problems
 Enrichment Tasks: The Random Walk  Cell Phones
Construct and compare linear and exponential models and solve problems.
F.LE.A.2
Construct exponential functions, including geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table) (SAT® Content  PAM.01).
 Check for Understanding: Linear vs Exponential Growth
 Review/Rewind: Intro to Exponential Functions
 Enrichment Tasks: Snail Invasion  Basketball Bounces, Assessment Variation 2
Interpret expressions for functions in terms of the situations they model.
F.LE.B.5
Interpret the parameters in an exponential function in terms of a context (SAT® Content  PAM.12).
 Check for Understanding: Comparing Linear Functions Applications  Modeling with Exponential Functions
 Review/Rewind: Linear vs Exponential Growth from Data
 Enrichment Tasks: Illegal Fish  Newton's Law of Cooling
Write expressions in equivalent forms to solve problems.
A.SSE.B.4
Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.
 Check for Understanding: Calculating Finite Geometric Series  Finite Geometric Series Word Problems
 Review/Rewind: Intro to Geometric Series  Sigma Notation for Sums
 Enrichment Tasks: YouTube Explosion  A Lifetime of Savings
Build new functions from existing functions.
F.BF.B.4
Find inverse functions. Focus on linear functions, but consider simple situations where the domain of the function must be restricted in order for the inverse to exist, such as f(x) = x^2, x > 0.
a. Solve an equation of the form f(x) = c. For example, f(x) = 2x^3 or f(x) = (x + 1)/(x – 1) for x ≠ 1.
 Check for Understanding: Inverses of Linear Functions  Understanding Inverses of Functions
 Review/Rewind: Intro to Inverse Functions
 Enrichment Tasks: Invertible or Not?  US Households
Analyze functions using different representations.
F.IF.C.7
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*
e. Graph exponential and logarithmic functions, showing intercepts and end behavior.
 Check for Understanding: Graphs of Exponentials and Logarithms
 Review/Rewind: Review 8 Types of Functions and Their Graphs  Graphs of Exponentials and Logarithms
 Enrichment Tasks: Identifying Graphs of Functions  Modeling London's Population
Interpret functions that arise in applications in terms of a context.
F.IF.B.4
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*
 Check for Understanding: Interpreting Features of Functions  Positive and Negative Parts of Functions
 Review/Rewind: Key Features of a Graph Review
 Enrichment Tasks: Logistic Growth Model, Explicit Version  Influenza Epidemic
Interpret linear and exponential functions that arise in applications in terms of a context.
F.IF.B.6
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
 Check for Understanding: Average Rate of Change
 Review/Rewind: Finding Slope from Two Points  Introduction to the Average Rate of Change
 Enrichment Tasks: Mathemafish Population  The High School Gym
Analyze functions using different representations.
F.IF.C.9
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
 Check for Understanding: Comparing Features of Functions
 Review/Rewind: Comparing Features of Functions Review  Graphing in SlopeIntercept Form Review
 Enrichment Tasks: Throwing Baseballs
Build a function that models a relationship between two quantities.
F.BF.A.1
Write a function that describes a relationship between two quantities.*
b. Combine standard function types using arithmetic operations.
 Check for Understanding: Modeling with OneVariable Equations and Inequalities
 Review/Rewind: Modeling with Linear Relationships  Modeling with OneVariable Equations and Inequalities
 Enrichment Tasks: Sum of Functions  Kimi and Jordan
Write expressions in equivalent forms to solve problems
A.SSE.B.3
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
c. Use the properties of exponents to transform expressions for exponential functions.
 Check for Understanding: Equivalent Forms of Exponential Expressions  Rewriting and Interpreting Exponential Functions
 Review/Rewind: Initial Value and Common Ratio of Exponential Functions
Build new functions from existing functions.
F.BF.B.3
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
 Check for Understanding: Even and Odd Functions  Shifting and Reflecting Functions
 Review/Rewind: Stretching Functions  Types of Transformations
 Enrichment Tasks: Transforming the Graph of a Function  Building an Explicit Quadratic Function By Composition
Represent and solve equations graphically.
A.REI.D.11
Explain why the xcoordinates of the points where the graphs of the equations y=f(x) and y=g(x) intersect are the solutions of the equation f(x)=g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, exponential, and logarithmic functions.*
 Check for Understanding: Intersecting Functions  Systems of Nonlinear Equations
 Review/Rewind: Solving a System of Equations by Graphing  Solving Equations by Graphing (nonlinear)
 Enrichment Tasks: Ideal Gas Law  Introduction to Polynomials  College Fund
Construct and compare linear, quadratic, and exponential models and solve problems.
F.LE.A.4
For exponential models, express as a logarithm the solution to a b^ct = d, where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.
 Check for Understanding: Using Logarithms to Solve Exponential Equations
 Review/Rewind: Solving Exponential Equations with Logarithms (base  10)
 Enrichment Tasks: Exponential Kiss  Graphene
What are some signs of student mastery?

Tools & Technology
Desmos is a free online graphing calculator that works on any computer or tablet without requiring any downloads. A FREE Desmos iPad app is available too! Try the Geometric Sequence Calculator! Interested in exploring more with series? Check out the Convergence Calculator. If you'd like to visualize functions and their inverses, look at the Inverse Function Calculator from Wolfram! 