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- https://math.libretexts.org/Courses/Lorain_County_Community_College/Book%3A_Precalculus_Jeffy_Edits_3.75/01%3A_Relations_and_Functions/1.07%3A_TransformationsIn this section, we study how the graphs of functions change, or transform, when certain specialized modifications are made to their formulas. The transformations we will study fall into three broad c...In this section, we study how the graphs of functions change, or transform, when certain specialized modifications are made to their formulas. The transformations we will study fall into three broad categories: shifts, reflections and scalings, and we will present them in that order.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_370%3A_Precalculus/01%3A_Relations_and_Functions/1.07%3A_TransformationsThis section covers transformations of functions, including translations, reflections, stretches, and compressions. It explains how to apply these transformations to function graphs and how changes in...This section covers transformations of functions, including translations, reflections, stretches, and compressions. It explains how to apply these transformations to function graphs and how changes in function equations affect their graphs. The section provides examples and visual aids to illustrate vertical and horizontal shifts, reflections over the axes, and scaling of graphs. These concepts help understand how functions can be manipulated to model different real-world scenarios.
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/03%3A_Linear_Transformations_and_Matrix_Algebra/3.02%3A_One-to-one_and_Onto_TransformationsThis page discusses the concepts of one-to-one and onto transformations in linear algebra, focusing on matrix transformations. It defines one-to-one as each output having at most one input and outline...This page discusses the concepts of one-to-one and onto transformations in linear algebra, focusing on matrix transformations. It defines one-to-one as each output having at most one input and outlines examples and theorems related to this property. The text emphasizes that a transformation is onto if every output corresponds to some input.
- https://math.libretexts.org/Courses/Highline_College/MATH_141%3A_Precalculus_I_(2nd_Edition)/02%3A_Inequalities_and_Functions/2.07%3A_Transformations_of_FunctionsThe graph of h has transformed f in two ways: f(x+1) is a change on the inside of the function, giving a horizontal shift left by 1, and the subtraction by 3 in f(x+1)−3 is a change to...The graph of h has transformed f in two ways: f(x+1) is a change on the inside of the function, giving a horizontal shift left by 1, and the subtraction by 3 in f(x+1)−3 is a change to the outside of the function, giving a vertical shift down by 3. For h(x), the negative sign inside the function indicates a horizontal reflection, so each input value will be the opposite of the original input value and the h(x) values stay the same as the f(x) values.
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_(Stitz-Zeager)/01%3A_Relations_and_Functions/1.07%3A_TransformationsIn this section, we study how the graphs of functions change, or transform, when certain specialized modifications are made to their formulas. The transformations we will study fall into three broad c...In this section, we study how the graphs of functions change, or transform, when certain specialized modifications are made to their formulas. The transformations we will study fall into three broad categories: shifts, reflections and scalings, and we will present them in that order.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_384%3A_Foundations_for_Calculus/01%3A_Functions_-_Fundamental_Concepts/1.05%3A_TransformationsIn this section, we study how the graphs of functions change, or transform, when certain specialized modifications are made to their formulas. The transformations we will study fall into three broad c...In this section, we study how the graphs of functions change, or transform, when certain specialized modifications are made to their formulas. The transformations we will study fall into three broad categories: shifts, reflections and scalings, and we will present them in that order.
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/07%3A_Appendix/7.02%3A_B_-_NotationThis page includes a table detailing mathematical symbols, their meanings, and first appearances in a book. It covers symbols for numbers, matrices, transformations, vector spaces, and complex numbers...This page includes a table detailing mathematical symbols, their meanings, and first appearances in a book. It covers symbols for numbers, matrices, transformations, vector spaces, and complex numbers, providing readers with a quick reference to understand the notation used in various mathematical concepts.
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/03%3A_Linear_Transformations_and_Matrix_Algebra/3.04%3A_Matrix_MultiplicationThis page explores the interplay between compositions of transformations and matrix multiplication in linear algebra. It defines the composition of transformations, illustrates their properties, inclu...This page explores the interplay between compositions of transformations and matrix multiplication in linear algebra. It defines the composition of transformations, illustrates their properties, including non-commutativity and associativity, and connects these concepts to matrix operations. The Row-Column Rule for matrix multiplication is explained, alongside the implications of this non-commutative nature.
- https://math.libretexts.org/Courses/Coastline_College/Math_C097%3A_Support_for_Precalculus_Corequisite%3A_MATH_C170/1.03%3A_Inequalities_and_Functions/1.3.07%3A_Transformations_of_FunctionsThe graph of h has transformed f in two ways: f(x+1) is a change on the inside of the function, giving a horizontal shift left by 1, and the subtraction by 3 in f(x+1)−3 is a change to...The graph of h has transformed f in two ways: f(x+1) is a change on the inside of the function, giving a horizontal shift left by 1, and the subtraction by 3 in f(x+1)−3 is a change to the outside of the function, giving a vertical shift down by 3. For h(x), the negative sign inside the function indicates a horizontal reflection, so each input value will be the opposite of the original input value and the h(x) values stay the same as the f(x) values.
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/04%3A_Determinants/4.03%3A_Determinants_and_VolumesThis page explores the connections between matrices, their determinants, and geometric volumes, focusing on parallelepipeds. It defines parallelepipeds and illustrates how the determinant relates to t...This page explores the connections between matrices, their determinants, and geometric volumes, focusing on parallelepipeds. It defines parallelepipeds and illustrates how the determinant relates to their volume, covering key determinant properties and their impact on area and volume calculations for parallelograms and triangles. The text demonstrates how linear transformations scale volumes by the absolute value of the determinant.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_372%3A_College_Algebra_for_Calculus/01%3A_Refining_Function_Knowledge/1.04%3A_Graphing_Functions_Using_TransformationsIn this section, we study how the graphs of functions change, or transform, when certain specialized modifications are made to their formulas. The transformations we will study fall into three broad c...In this section, we study how the graphs of functions change, or transform, when certain specialized modifications are made to their formulas. The transformations we will study fall into three broad categories: shifts, reflections and scalings, and we will present them in that order.
