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AMC 10/12
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Textbook
Introduction
1. Algebra
1.1 Manipulation
1.2 Functions (polynomial)
1.3 Functions (trigonometric)
1.4 Functions (exponential and logarithmic)
1.5 Functions (sequences)
1.6 Functions (other)
2. Geometry
3. Number theory
4. Probability
5. Combinatorics
6. What's next?
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1.6 Functions (other)
Achievable AMC 10/12
1. Algebra

Functions (other)

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Miscellaneous knowledge about functions

The AMC tests a few other facts that fall under “functions” but which don’t fit into any of the other categories above. They are:

  1. The existence, form, and definition of piecewise functions
  2. The strategy of beginning the analysis of a piecewise function by examining its behavior on the boundaries between its pieces
  3. The definition of a cyclic function

What to do

There’s very little here, and it will be easy to learn, so just take the quiz to ensure that you do know it!

Piecewise functions

  • Defined by different expressions over distinct intervals
  • Each “piece” applies to a specific domain subset

Analyzing piecewise functions

  • Start by examining behavior at boundaries between pieces
  • Check for continuity and value agreement at interval endpoints

Cyclic functions

  • Functions that repeat values in a fixed cycle
  • Example: f(n) = f(n + k) for some period k

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Functions (other)

Miscellaneous knowledge about functions

The AMC tests a few other facts that fall under “functions” but which don’t fit into any of the other categories above. They are:

  1. The existence, form, and definition of piecewise functions
  2. The strategy of beginning the analysis of a piecewise function by examining its behavior on the boundaries between its pieces
  3. The definition of a cyclic function

What to do

There’s very little here, and it will be easy to learn, so just take the quiz to ensure that you do know it!

Key points

Piecewise functions

  • Defined by different expressions over distinct intervals
  • Each “piece” applies to a specific domain subset

Analyzing piecewise functions

  • Start by examining behavior at boundaries between pieces
  • Check for continuity and value agreement at interval endpoints

Cyclic functions

  • Functions that repeat values in a fixed cycle
  • Example: f(n) = f(n + k) for some period k