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### Chapter 4--Functions, Relations, Transformations

 Essential Question:  What is the relationship between transformations and their equations and graphs? Unit Rationale:  Interpretation of graphs of functions and relations, including using function notation and function families, is a prerequisite to applying transformation to those graphs. As a result of this unit, students will be able to: Ø  Write the equation from graphs using transformation Ø  Graph the transforms equation Ø  Identify domain and range for a function Ø  Use and understand function notation Ø  Apply transformation concepts to model situations Vocabulary: ·         Relation, function ·         Transformations, image ·         Discrete, continuous ·         Function notation ·         Translation, reflection, dilation ·         Parabola ·         Line of symmetry ·         Vertex ·         Parent function ·         Quadratic function ·         Square root function ·         Absolute value function Focus Standards: A2.1.C  Solve problems that can be represented by quadratic functions and equations. A2.5.A  Construct new functions using transformation f(x-h), f(x) +k, CF(x) and by adding and subtracting functions and describe the effect on the original graph A2.5.B  Plot points, sketch, and describe the graphs of functions of the form f(x)=a (x-c)^1/2 +d, and solve related equations. Support Standards: A2.1.A  Select and justify functions and equations to model and solve problems. Reasoning, Problem Solving, and Communication Standards: A2.8.D  Generalize a solution strategy for a single problem to a class of related problems, and apply a strategy for a class of related problems to solve specific problems. A2.8.E  Read and interpret diagrams, graphs, and text containing the symbols, language and conventions of mathematics.