In mathematics, the graph of a function is the set of ordered pairs , where In the common case where and are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane. In the case of functions of two variables, that is functions whose domain consists of pairs the graph usually refers to the set of ordered triples where instead of the pairs as in the definition above. This set is a subset of three-dimensional space; for a continuous real-valued function of two real variables, it is a surface. In science, engineering, technology, finance, and other areas, graphs are tools used for many purposes. In the simplest case one variable is plotted as a function of another, typically using rectangular axes; see Plot (graphics) for details. A graph of a function is a special case of a relation. In the modern foundations of mathematics, and, typically, in set theory, a function is actually equal to its graph. However, it is often useful to see functions as mappings, which consist not only of the relation between input and output, but also which set is the domain, and which set is the codomain. For example, to say that a function is onto (surjective) or not the codomain should be taken into account. The graph of a function on its own doesn't determine the codomain. It is common to use both terms function and graph of a function since even if considered the same object, they indicate viewing it from a different perspective. (Wikipedia).
What are the important things to know about the graph of a function
๐ Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
๐ Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
How to determine the characteristics of a functions graph
๐ Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
Using the vertical line test to determine if a graph is a function or not
๐ Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
๐ Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
๐ Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
๐ Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
๐ Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
How to determine if 3 graphs represent a function and determine domain range
๐ Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
Irina Gelbukh 2023: The Reeb graph of a smooth function encodes the function class and manifold type
Title: How the Reeb graph of a smooth function encodes the class of the function and the type of the manifold Abstract: The Reeb graph of a function is a space obtained by contracting connected components of the function's level sets to points. Computer scientists mostly deal with Morse f
From playlist Vietoris-Rips Seminar
Lec 03. Fundamental Graphs & Symmetry College Algebra with Dennis Allison
See full course at: https://cosmolearning.org/courses/college-algebra-pre-calculus-with-dennis-allison/ Video taken from: http://desource.uvu.edu/videos/math1050.php Lecture by Dennis Allison from Utah Valley University.
From playlist UVU: College Algebra with Dennis Allison | CosmoLearning Math
LambdaConf 2015 - Loom and Functional Graphs in Clojure Aysylu Greenberg
Graphs are ubiquitous data structures, and the algorithms for analyzing them are fascinating. Loom is an open-source Clojure library that provides many graph algorithms and visualizations. We will discuss how graphs are represented in a functional world, bridge the gap between procedural d
From playlist LambdaConf 2015
Quadratic Function Transformations
This video explains transformation of the basic quadratic function. http://mathispower4u.com
From playlist Determining Transformations of Functions
Lec 16. Exponential Functions College Algebra with Dennis Allison
See full course at: https://cosmolearning.org/courses/college-algebra-pre-calculus-with-dennis-allison/ Video taken from: http://desource.uvu.edu/videos/math1050.php Lecture by Dennis Allison from Utah Valley University.
From playlist UVU: College Algebra with Dennis Allison | CosmoLearning Math
Introduction to Hyperbolic Functions
This video provides a basic overview of hyperbolic function. The lesson defines the hyperbolic functions, shows the graphs of the hyperbolic functions, and gives the properties of hyperbolic functions.
From playlist Using the Properties of Hyperbolic Functions
Introduction to Hyperbolic Functions
This video provides a basic overview of hyperbolic function. The lesson defines the hyperbolic functions, shows the graphs of the hyperbolic functions, and gives the properties of hyperbolic functions. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Differentiation of Hyperbolic Functions
Lec 04. Transformations and More College Algebra with Dennis Allison
See full course at: https://cosmolearning.org/courses/college-algebra-pre-calculus-with-dennis-allison/ Video taken from: http://desource.uvu.edu/videos/math1050.php Lecture by Dennis Allison from Utah Valley University.
From playlist UVU: College Algebra with Dennis Allison | CosmoLearning Math
Lec 09. Polynomial Functions College Algebra with Dennis Allison
See full course at: https://cosmolearning.org/courses/college-algebra-pre-calculus-with-dennis-allison/ Video taken from: http://desource.uvu.edu/videos/math1050.php Lecture by Dennis Allison from Utah Valley University.
From playlist UVU: College Algebra with Dennis Allison | CosmoLearning Math
When is a function bounded below?
๐ Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
Extremal theory of ordered graphs โ Gรกbor Tardos โ ICM2018
Combinatorics Invited Lecture 13.3 Extremal theory of ordered graphs Gรกbor Tardos Abstract: We call simple graphs with a linear order on the vertices โordered graphsโ. Turรกn-type extremal graph theory naturally extends to ordered graphs. This is a survey on the ongoing research in the ex
From playlist Combinatorics