Library of Functions

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The Library of Functions is a collection of functions for which you should know the basic properties and shape of graph. The section is finished off with a discussion of piecewise-defined functions.

Library of Functions

1) Constant Function: Constant functions have the form f(x) = b where b is a real number.

Properties: Domain: , Range is b, and the function is constant.

2) Identity function: f(x) = x

Properties: Domain = Range =

3) Square Function:

Properties: Domain = , while the range is . This function is also even.

4) Cube Function:

Properties: Domain = Range = . is an odd function too.

5) Square Root Function:

Properties: The domain and range are both .

6) Cube Root Function:

Properties: This function is odd and the domain = range =

7) Reciprocal Function:

Properties: The domain is . The range is also the same.

8) Absolute Value Function:

Properties: Domain = , Range = . This function is also even.

Piecewise-defined Functions

A piecewise-defined function is a function that takes on the values of different functions depending on the x-value.

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