## Reflection: Continuous Assessment Inverse Functions - Section 3: Group Work

In the class presentation, students are presented with a definition of inverse functions verbally (“a function that undoes another), symbolically (f(f-1(x))=x), graphically, and as a relationship presented in tables of values. These multiple representations are meant to help clarify the big idea of inverse functions, but can sometimes confuse students too.

This task offers students an opportunity to develop their understanding by demonstrating all of these representations while exploring one function at a time. They must represent the inverse function in its symbolic form, identify the domain and range of both function and inverse, make a table of values for each that demonstrates inverses, and graph both functions together. By working in groups, they can self-check along the way and I can quickly assess which groups might need more assistance from me. Using a task that shows one function with its inverse demonstrated four ways, rather than four functions each with inverses represented differently, allows students to continually self-assess. Once they can envision what an inverse function might look like in one of the four representations, they can ‘translate’ this idea to another representation even if they don’t fully understand it. For example, they may be able to see that f(x) = 2x - 3 and f-1(x) = (x+3)/2 are indeed inverses, but they may need to make a table of values for each function and graph the resulting ordered pairs in order to see the relationship in its tabular and graphical representations. I find that their understanding quickly grows and solidifies.

Using Multiple Representations
Continuous Assessment: Using Multiple Representations

# Inverse Functions

Unit 5: Rational and Inverse Functions
Lesson 6 of 8

## Big Idea: A function performs a series of operations on the input to produce and output; an inverse function undoes all of these operations in the reverse order they were performed.

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Standards:
Subject(s):
Math, composite function, inverse functions, Algebra, domain, range, inverse operations
90 minutes

### Colleen Werner

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