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Common Core (Functions)

Common Core for Mathematics

Examples, solutions, videos, and lessons to help High School students understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

Common Core: HSF-IF.A.1

The following diagram give the graphs, domain, and range of some functions. Scroll down the page for more examples and solutions.

**The Domain and Range of 9 Basic Functions**

This video quickly reviews the domain and range of nine basic functions.

Constant Function, Identity Function, Absolute Value Function, Quadratic Function, Cubic Function, Square Root Function, Cube Root Function, Reciprocal Function, Squared Reciprocal Function.

**Ex: Determine the Domain of an Absolute Value Function**

This video provides an example of how to determine the domain of an absolute value function.

Ex: The Domain of Rational Functions

This video provides 3 examples of how to determine the domain of a rational function. The domain is express in words, a graph, and using interval notation.

**Ex: Determine the Domain and Range of a Rational Function**

This video provides an example of how to determine the domain of a rational function.

Ex: Determine the Domain and Range of a Square Root Function

This video provides an example of how to determine the domain of a square root function.

**Ex: Domain and Range of Square Root Functions**

This video provided three examples of how to determine the domain and range of various square root functions. The results are verified graphically.

**Ex: Domain of a Square Root Function with a Quadratic Radicand**

This video explains several ways to find the domain of a square root function when the radicand is a quadratic function.

**Ex: Domain and Range of Radical Functions**

This video provided examples of how to find the domain and range of radical functions with index 2, 3, and 4. The results are checked graphically.

**Ex: The Domain of a Function Containing a Square Root and a Denominator**

This video explains how to determine the domain of a function that contains a square root and denominator.

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