Function basics

Decide whether each input has one output and distinguish domains, ranges, and values.

Meaning

A function assigns one element of its codomain to each element of its domain. The range is the set of actual outputs and may be only part of the codomain.

Example

For on all real inputs, Even with all reals as codomain, the range is the nonnegative reals.A real square is nonnegative, so negative outputs cannot occur. Conversely, any y≥0 is obtained from x=√y, so the range is exactly the nonnegative reals.Different inputs may have the same output. One input cannot have two different outputs in a function.

Practice for this concept

Scope and references

Topics

Functions, domains, codomains, ranges, function values

Learning goal

Decide whether each input has one output and distinguish domains, ranges, and values.

Helpful background

Explore correspondence and the meaning of inputs and outputs.

Basic function concepts

These ordinary choice questions provide limited practice in this concept. They do not establish independent solution, full-concept performance, or mastery.

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