Overview
On this page, we introduce function notation and operations on functions.
Basic Learning Objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
- Understand the idea of a function as a machine that takes inputs and produces outputs.
- Evaluate a function at a given numerical input.
- Perform arithmetical operations (addition, subtraction, multiplication, and division) on functions.
Advanced Learning Objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
- Find the domain of a function defined as an algebraic expression.
- Evaluate a function at an algebraic expression and peform composition of functions.
To prepare for class
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Watch the following videos (by Tyler Wallace) which introduce the basics of function notation and show how to evaluate a function at various inputs:
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Watch the following video (by Tyler Wallace) which show how to perform arithmetical operations on functions:
After class
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Watch the following video (by Tyler Wallace) which shows how to find the domain of a function defined as an algebraic expression:
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Watch the following video (by patrickJMT) which gives more examples of finding the domain of a function defined as an algebraic expression:
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Watch the following videos (by Tyler Wallace) which show how to compute the composition of two functions:
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Watch the following videos (by patrickJMT) which show how to compute the composition of two functions:
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Watch the following videos (by Mario’s Math Tutoring) which show how to compute the composition of two functions: