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- https://math.libretexts.org/Bookshelves/Algebra/Supplemental_Modules_(Algebra)/Elementary_algebra/1%3A_Functions/1.2%3A_Graphs_and_SymmetryWe say that a graph is symmetric with respect to the origin if for every point (a,b) on the graph, there is also a point (−a,−b) on the graph; hence f(x,y)=f(−x,−y). To test algebraicall...We say that a graph is symmetric with respect to the origin if for every point (a,b) on the graph, there is also a point (−a,−b) on the graph; hence f(x,y)=f(−x,−y). To test algebraically if a graph is symmetric with respect to the origin we replace both x and y with −x and −y and see if the result is equivalent to the original expression.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_372%3A_College_Algebra_for_Calculus/11%3A_Appendix_-_Prerequisite_Function_Material/11.01%3A_Sets_of_Real_Numbers_and_the_Cartesian_Coordinate_PlaneThis section introduces the sets of real numbers, their properties, and the Cartesian coordinate plane. It covers the classification of numbers (natural, whole, integers, rational, and irrational) and...This section introduces the sets of real numbers, their properties, and the Cartesian coordinate plane. It covers the classification of numbers (natural, whole, integers, rational, and irrational) and explains how to plot points and graph equations on the Cartesian plane. The section also discusses intervals and the distance formula, providing foundational knowledge for working with functions and graphs in Algebra.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_372%3A_College_Algebra_(Lecture_Notes)/01%3A_Functions/1.02%3A_Domain_and_RangeFinding the Domain of a Function Defined by an Equation Examples Domain and range of a set of data points. Domain of a quadratic, simple rational, and shifted square root function. Note You will likel...Finding the Domain of a Function Defined by an Equation Examples Domain and range of a set of data points. Domain of a quadratic, simple rational, and shifted square root function. Note You will likely have to review interval notation. Definitions Set-builder notation Finding Domain and Range from Graphs Do one. Finding Domains and Ranges of the Toolkit Functions Graphing Piecewise-Defined Functions Definition Piecewise function Example Graph a piecewise involving raw toolkit functions only.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_370%3A_Precalculus/01%3A_Relations_and_Functions/1.01%3A_Sets_of_Real_Numbers_and_the_Cartesian_Coordinate_PlaneThis section introduces the sets of real numbers, their properties, and the Cartesian coordinate plane. It covers the classification of numbers (natural, whole, integers, rational, and irrational) and...This section introduces the sets of real numbers, their properties, and the Cartesian coordinate plane. It covers the classification of numbers (natural, whole, integers, rational, and irrational) and explains how to plot points and graph equations on the Cartesian plane. The section also discusses intervals and the distance formula, providing foundational knowledge for working with functions and graphs in Algebra.
