Exponential Functions

13 Components
Initial Task
Multiplying Cells
Big Ideas
Big Idea 1 Big Idea 2 Big Idea 3 Big Idea 4 Big Idea 5
Formative Assessment Lesson
Selecting a formative assessment lesson for Algebra II Unit 2 Comparing Investments Having Kittens
Re-engagement
Re-engagement for Unit 2
End of Unit Assessments
End of Unit Assessment for Unit 2 End of Unit Assessment Teacher Resources ALG II Unit 2 Find aligned Regents questions with Quiz Banker
A2 U2: Exponential Functions
Browse Components
Initial Task
Multiplying Cells
Big Ideas
Big Idea 1 Big Idea 2 Big Idea 3 Big Idea 4 Big Idea 5
Formative Assessment Lesson
Selecting a formative assessment lesson for Algebra II Unit 2 Comparing Investments Having Kittens
Re-engagement
Re-engagement for Unit 2
End of Unit Assessments
End of Unit Assessment for Unit 2 End of Unit Assessment Teacher Resources ALG II Unit 2 Find aligned Regents questions with Quiz Banker
Big Idea:

Big Idea 4

A logarithm is the inverse of an exponential function.

1 week
See Standards
Common Core: Supporting Standards:
F-IF.C.7e

Analyze functions using different representations. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

F-LE.A.4

Construct and compare linear, quadratic, and exponential models and solve problems. For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

Common Core: Additional Standards:
F-BF.B.4a

Build new functions from existing functions. Find inverse functions: Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2x3 or f(x) = (x+1)/(x-1) for x ≠ 1.

Common Core: Plus Standards:
F-BF.B.4b(+)

Build new functions from existing functions.  Find inverse functions: Verify by composition that one function is the inverse of another.

F-BF.B.4c(+)

Build new functions from existing functions. Find inverse functions: Read values of an inverse function from a graph or a table, given that the function has an inverse.

Evidence of Understanding

  • describe an input in terms of its corresponding output
    • approximate and justify the input of an exponential function given the output
      • Example: given 59 = 2x, students recognize 2xas a continuous function and that 59 is between 32 and 64 and therefore x is a value between 5 and 6, closer to 6
    • describe an exponential function in terms of the output, f(x), and its base
      • Example: f(x) = 2x can be described as “base 2 is f(x) when raised to the exponent x” or “f(x) is equivalent to the base 2 raised to exponent x”
    • use the outputs of an exponential function to graph its inverse function
      • create and analyze a table of values for the inverse function
      • describe the intercepts and end behavior of the inverse function
  • create equivalent representations for exponential and logarithmic functions
    • analyze relationships between exponential and logarithmic equations using graphs or tables
      • Example: compare Y= 2x, log2Y= X, and log2X = Y using features from their graphs
      • recognize when equations model the same function, inverse functions, or neither
    • create a table or graph from a simple logarithmic function rule (including natural logarithm)
      • determine the output of a simple logarithm without a calculator (Example: log327 is 3 or log216 is 4 or log418 is a number slightly more than 2)
    • create a simple exponential or logarithmic function rule that best models a given graph or table
    • justify connections between features of the table, graph, and function rule of a given logarithm
  • illustrate exponentials and logarithms are inverse functions
    • prove the composition of an exponential function and its inverse log function are commutative
    • prove an exponential function and its inverse log function map onto one another over y = x
      • describe how an exponential function is the reflection of its inverse log function
    • algebraically solve for the inverse function rule for an exponential or log function

Develop conceptual understanding:

inverse, logarithm, natural logarithm

Supporting terms to communicate:

function, input, output, domain, range, exponential, base, e, natural base, intercept, end behavior, asymptote, inverse, commutative, reflect 

Core Resource

There is no Core Resource for this Big Idea.

Consider using the Instructional Routines linked below for teaching towards this Big Idea.