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Function

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College Algebra

Definition

A function is a relation between a set of inputs and a set of permissible outputs such that each input is related to exactly one output. Functions are often represented by $f(x)$ where $x$ is the input variable.

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5 Must Know Facts For Your Next Test

  1. A function can be defined using different types of expressions such as equations, tables, and graphs.
  2. The domain of a function is the complete set of possible input values (x-values) that produce valid outputs.
  3. The range of a function is the complete set of all possible resulting output values (y-values).
  4. A function passes the vertical line test if no vertical line intersects its graph more than once.
  5. Function notation $f(x)$ specifies that $f$ is a function with $x$ as its input variable.

Review Questions

  • What does the vertical line test determine about a graph?
  • How do you find the domain and range of a given function?
  • What does $f(x)$ mean in terms of functions?
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