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Formative Assessment Lesson
Re-engagement
End of Unit Assessments
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Big Ideas
Formative Assessment Lesson
Re-engagement
End of Unit Assessments
Big Idea:

### An inverse function is a function that "undoes" another function; if f(x) maps x to y, then its inverse maps y back to x.

1 week

Evidence of Understanding

• use composition of functions to prove that two functions are inverses
• justify why the output of the composition of inverse functions is the input
• describe how operations on the function's domain are counterbalanced in its inverse function
• explain why quadratic and square root functions are inverses
• Example: y = 2x2 - 5 has an inverse with +5,½, and a square root
• only inverse functions have commutative compositions

• create a function’s inverse using a graph or table of values
• justify two functions are inverses using specific points from the tables of each function
• describe the general shape and characteristics of a given function's inverse
• use multiple representations of a function to help illuminate characteristics of its inverse
• given a function's graph, create a graph or table of values for its inverse function
• determine whether a function is one to one and has an inverse function
• explain when domain needs to be restricted to produce an inverse and state the restriction (radical functions and the difference between square root and cube root)
• explain why inverse functions reflect over the line y = x

• generate an equation for the inverse of a function and use it to solve problems
• confirm two equations are inverses using compositions of functions or the reflection over y = x
• given a function's graph or table of values, create and justify the function's inverse equation
• use rate of change and other key characteristics to create the inverse equation
• algebraically generate the inverse equation (Note: only for simple polynomials- especially linear, quadratic and cubic, or their inverses- radical, cube root, etc.)
• use the inverse equation to describe qualities about the graph or table of f(x) or f-1(x)
• solve square root equations and explain extraneous solutions

Develop conceptual understanding:

inverse function, commutative, one to one, radical function, square root, cube root, reflect, extraneous solution

Supporting terms to communicate:

composition, input, output, independent, dependent, domain, range, symmetry, linear, quadratic, cubic

Core Resource
A core resource supports multiple days of instruction.
• Investigating Inverses
This is a multi-day resource to support students in understanding different methods for determining if two functions are inverses and how each of those methods are related.
Resource:
Investigating Inverses

This is a multi-day resource to support students in understanding different methods for determining if two functions are inverses and how each of those methods are related.

All Resources From:
• Unit 1

#### Families of Functions

Instructional Routine: Connecting Representations
These tasks are embedded within the instructional routine called Connecting Representations.
• Inverse functions and graphs
Students will connect reflecting a function on a graph to creating the inverse function of the function.
Resource:
Inverse functions and graphs

Students will connect reflecting a function on a graph to creating the inverse function of the function.

All Resources From:
• Unit 1