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F-BF

MAT-HS.F-BF.02

MAT-HS Targeted Standards
(F) Concept: Function
(BF) Domain: Building Functions
Cluster: Build a function that models a relationship between two quantities

MAT-HS.F-BF.02 Write a function that describes a relationship between two quantities.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can make connections between linear functions and arithmetic sequences, and exponential functions and geometric sequences.

Product Targets

  • I can write and translate between the recursive and explicit formula for a arithmetic sequence and use the formulas to model a situation.
  • I can write and translate between the recursive and explicit formula for a geometric sequence and use the formulas to model a situation.

Proficiency Scale

Score   Description Sample Activity
4.0 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. -
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 “The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. -
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).
2.0 The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). -
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).
1.0 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). -
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill. -

Resources

Web

Vocab

  • sequence
  • arithmetic sequences
  • geometric sequences

MAT-HS.F-BF.03

MAT-HS Targeted Standards
(F) Concept: Function
(BF) Domain: Building Functions
Cluster: Build new functions from existing functions.

MAT-HS.F-BF.03*   Identify the effect on the graph of replacing f(x) by f(x) + k, f(x + k), k f(x), and f(kx), for specific values of k (both positive and negative); find the value of k given the graphs. Recognize even and odd functions from their graphs.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can experiment to identify, using technology, the transformational effects on the graph of a function f(x) when f(x) is replaced by f(x)+k, k∙f(x), f(kx), and f(x+k) for specific values of k, both positive and negative.
  • I can find the value of k given the graph of a transformed function.
  • I can recognize even and odd functions from their graphs and equations.

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity

4.0

(advanced)

 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. Write three different quadratic functions whose graphs have the line x = 4 as an axis of symmetry but have different y-intercepts.
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.

3.0

(proficient)

 The student can:
  • analyze the transformational effects on the graph of a function.
  • find the value of k given the graph of a transformed function.
  • determine whether a function is even or odd given a graph.
The student exhibits no major errors or omissions.

Describe all the transformations and graph the function.

 
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).

2.0

(progressing)

 There are no major errors or omissions regarding the simpler details and processes as the student can:
  • recognize and recall specific terminology, such as:
    • vertical shift
    • horizontal shift
    • compress/amplified
    • stretch/shrink
    • reflection
    • even function
    • odd function
 However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 

Given the graph, identify all of the transformations.
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).

1.0

(beginning)

 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content).  
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill.  

Resources

Web

Vocab

  • transformation
  • even functions
  • odd functions

MAT-HS.F-BF.04

MAT-HS Targeted Standards
(F) Concept: Function
(BF) Domain: Building Functions
Cluster: Build new functions from existing functions

MAT-HS.F-BF.04 Find inverse functions.

  • a. 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) =2 x³ or f(x) = (x+1)/(x-1) for x ≠ 1.
  • b. Verify by composition that one function is the inverse of another.
  • c. Read values of an inverse function from a graph or a table, given that the function has an inverse.
  • d. Produce an invertible function from a non-invertible function by restricting the domain.

Student Learning Targets:

Knowledge Targets

  • I can recognize the notation for the composition of functions.
  • I can recognize the proper notation for inverse functions.

Reasoning Targets

  • I can determine the inverse of a function.
  • I can interpret the results of the horizontal line test.
  • I can verify whether two functions are inverses of each other using compositions.

Skills (Performance) Targets

  • I can perform composition of algebraic functions.
  • I can demonstrate the inverse of an algebraic function graphically.
  • I can perform the horizontal line test to determine if the inverse of a function exists.
  • I can find the inverse of a given function.
  • I can solve a function for the dependent variable and write the inverse of a function by interchanging the dependent and independent variables.

Product Targets

  • I can
  • I can

Proficiency Scale

Score   Description Sample Activity
4.0 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. -
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0 “The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. -
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).
2.0 The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). -
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).
1.0 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). -
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill. -

Resources

Web

Vocab

  • inverse function
  • independent variable
  • dependent variable

MAT-HS.F-BF.05

MAT-HS Targeted Standards
(F) Concept: Function
(BF) Domain: Building Functions
Cluster: Build new functions from existing functions

MAT-HS.F-BF.05 Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

Student Learning Targets:

Knowledge Targets

  • I can
  • I can

Reasoning Targets

  • I can
  • I can

Skills (Performance) Targets

  • I can
  • I can

Product Targets

  • I can
  • I can

Alg II Solve Logarithmic Equations Proficiency Scale

Score   Description Sample Activity

4.0

(advanced)

 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations.

Describe and correct the error in this work:
  3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.

3.0

(proficient)

 The student can:
  • solve a logarithmic equation and recognize an extraneous solution.
The student exhibits no major errors or omissions.

Solve the following logarithmic equation and check for extraneous solutions:

log3(x2-30)=log3(x)

  

Solve the following logarithmic equation and check for extraneous solutions:

2log2(x)=log2(4)+log2(x-1)
  2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).

2.0

(progressing)

 There are no major errors or omissions regarding the simpler details and processes as the student can:
  • recognize and recall specific terminology such as:
    • Base
    • Logarithm
    • Exponentiate
    • Condense
    • Expand
  • solve simple logarithmic equations.
  • evaluate a logarithmic expression.
  • use properties of logarithms to expand and condense an expression.
 However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

 

Solve the following logarithmic equation for x:

log10(100)=x
  1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).

1.0

(beginning)

 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). -
  0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).
0.0 Even with help, the student demonstrates no understanding or skill. -

Resources

Web
Vocab