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Algebra 2: Unit 4 Exponential and Logarithmic Functions
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last edited
by Christine Koerner 2 years, 9 months ago
Big Idea 1: Exponential functions are defined as f(x)=a^x

OASM: A2.A.1.2, A2.F.1.4, A2.D.1.2

Lessons and Additional Activities
Big Idea 1 Lessons 14 Overview (includes links to teacher notes and student activities)
Additional Activities
 XBOX Xponential (Mathalicious) Students create exponential models to predict the speed of video game processors over time, compare their predictions to observed speeds, and consider the consequences as digital simulations become increasingly lifelike.

Evidence of Understanding
Discover and describe characteristics of exponential functions in mathematical and real world situations.
Build exponential functions using information from a graph, table or situation.

Big Idea 2: Exponential functions share similar characteristics with power functions.

OASM:
A2.A.1.7,
A2.F.1.4,
A2.F.2.4

Lessons and Additional Activities
Big Idea 2 Lessons 14 Overview (includes links to teacher notes and student activities)

Evidence of Understanding
Compare and contrast the graphs of power and exponential functions.

Recognize differences and similarities of the graphs of power and exponential functions.

Identify appropriate situations to use exponential growth or decay functions, power functions, or none of these types given a graph, table, data points, sequence or real world scenario.
Compare and contrast the function rules of power and exponential functions.

Big Idea 3: Logarithms and exponents can be used to solve mathematical and realworld problems.


Lessons and Additional Activities
Big Idea 3 Lessons 14 Overview (includes links to teacher notes and student activities)

Evidence of Understanding
Discover and describe the relationship between an exponential function and a logarithmic function.

Compare and contrast the graphs of an exponential function and logarithmic function with the same base.

Create a logarithmic function when given an exponential function and vice versa. Justify that logarithmic functions and exponential functions are inverses of each other algebraically and graphically (ex. Use Desmos or graphing calculator.)
Recognize the necessity of converting an exponential function to logarithmic and vice versa when given a mathematical or real world situation.

Justify converting between exponential and logarithmic functions when solving for an unknown quantity.

Explore situations using technology that justify the equivalence of converting exponential and logarithmic functions.

Recognize restrictions or unnecessary domain and range values in mathematical and real world scenarios.

Identify the representation of input and output values for various scenarios.

Analyze the exponential or logarithmic model for the usefulness of the graph in its entirety for the given scenario. Use technology such as desmos or a graphing calculator.

Big Idea 4: Sequences can be described as functions. Sums of series can be represented by exponential and logarithmic functions

OASM: A2.A.1.7, A2.D.1.2

Lessons and Additional Activities
Big Idea 4 Lessons 14 Overview (includes links to teacher notes and student activities)

Evidence of Understanding
Discover patterns in sequences and identify as arithmetic, geometric or neither.
Discover and make generalizations about graphs of arithmetic and geometric sequences.
Build explicit and recursive formulas for geometric and arithmetic sequences.

Identify from a table, data set, graph or scenario as arithmetic or geometric sequence.

Research real world applications where explicit and recursive formulas are used.

Compare and contrast the graphs of explicit and recursive formulas. Identify when and how to use each.
Solve realworld and mathematical problems that can be modeled using arithmetic or finite geometric sequences or series given the nth terms and sum formulas.

Identify a sum formula as arithmetic or geometric.

Identify when and how to use both arithmetic and geometric sum formulas.

Recognize summation notation and identify key parts of the notation.

Algebra 2: Unit 4 Exponential and Logarithmic Functions

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