Symmetry - Daytona State College
... of the graph, then we also know the remaining portion of the graph as well. When we were graphing parabolas, we used this fact to get an extra point on some of the graphs. 1. A graph is said to be symmetric about the x-axisif whenever (a, b) is on the graph then so is (a, -b). Here is a sketch of a ...
... of the graph, then we also know the remaining portion of the graph as well. When we were graphing parabolas, we used this fact to get an extra point on some of the graphs. 1. A graph is said to be symmetric about the x-axisif whenever (a, b) is on the graph then so is (a, -b). Here is a sketch of a ...
Group representation theory
... Such considerations, when combined with the fact that σ 3 = id, make it clear that the product of any two elements of the set {id, σ, σ 2 , τ, στ, σ 2 τ } will always be another element of the same set. Furthermore, if σ i τ j = σ k τ l then σ i−k = τ l−j ; however, the only permutation which is bot ...
... Such considerations, when combined with the fact that σ 3 = id, make it clear that the product of any two elements of the set {id, σ, σ 2 , τ, στ, σ 2 τ } will always be another element of the same set. Furthermore, if σ i τ j = σ k τ l then σ i−k = τ l−j ; however, the only permutation which is bot ...
Quadratic Functions Extreme Values and Graphs
... • What is the graph of a quadratic function? • What is the vertex? The axis of symmetry? • The vertex and symmetry are important parts of the graph of a quadratic function. ...
... • What is the graph of a quadratic function? • What is the vertex? The axis of symmetry? • The vertex and symmetry are important parts of the graph of a quadratic function. ...
1.2 Graphs of Equations
... (-x)y3 + 10 = 0 Is this, or can we get this to look like -xy3 + 10 = 0 the original? No. x(-y)3 + 10 = 0 -xy3 + 10 = 0 Not like the original. (-x)(-y)3 + 10 = 0 This graph has origin symmetry. xy3 + 10 = 0 ...
... (-x)y3 + 10 = 0 Is this, or can we get this to look like -xy3 + 10 = 0 the original? No. x(-y)3 + 10 = 0 -xy3 + 10 = 0 Not like the original. (-x)(-y)3 + 10 = 0 This graph has origin symmetry. xy3 + 10 = 0 ...
Document
... (-x)y3 + 10 = 0 Is this, or can we get this to look like -xy3 + 10 = 0 the original? No. x(-y)3 + 10 = 0 -xy3 + 10 = 0 Not like the original. (-x)(-y)3 + 10 = 0 This graph has origin symmetry. xy3 + 10 = 0 ...
... (-x)y3 + 10 = 0 Is this, or can we get this to look like -xy3 + 10 = 0 the original? No. x(-y)3 + 10 = 0 -xy3 + 10 = 0 Not like the original. (-x)(-y)3 + 10 = 0 This graph has origin symmetry. xy3 + 10 = 0 ...
Groups part 1
... A Group is a set G with a binary operation that satisfies (G1) Closure: for all a,b G, a b G (G2) Associativity: for all a,b,c G, a (b c) = (a b) c (G3) Identity: there exists an element e G such that e a = a e = a for all a G. (G4) Inverses: for every a G, there exists a ...
... A Group is a set G with a binary operation that satisfies (G1) Closure: for all a,b G, a b G (G2) Associativity: for all a,b,c G, a (b c) = (a b) c (G3) Identity: there exists an element e G such that e a = a e = a for all a G. (G4) Inverses: for every a G, there exists a ...