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.