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### Chapter 7--Functions

 Essential Question:  How do we determine whether a graph, equation, or data set represents a function and what type of function a graph, equation, or data set represents? Unit Rationale:  Understanding and modeling with functions, building on students’ previous learning about linear and exponential relationships, helps us expand our understand of real-world situations using other non-linear models, setting the stage for deeper exploration in Algebra 2 and Pre-Calculus. As a result of this unit, students will be able to: Ø  Determine whether a relationship or set of data is a function; identify components such as domain, range, independent and dependent variables. Ø  Model functions with multiple representations, including graphs, tables, words, and symbols (using function notation). Ø  Identify, model and use specific types of functions such as absolute value and quadratic. Vocabulary: ·        Functions ·        Vertical line test ·        Independent variable ·        Dependent variable ·        Domain ·        Range ·        Increasing ·        Decreasing ·        Linear ·        Nonlinear ·        Discrete graph ·        Continuous graph ·        Absolute value function ·        Squaring function ·        Parabola ·        Step function ·        Discontinuous Standards: Standards will be assessed on both the state and classroom levels, however, standards with an asterisk (*) in the code will count for graduation requirements.  Focus Standards: *A1.3.A  Determine whether a relationship is a functions and identify the domain, range, roots, and independent and dependent variables. *A1.3.B  Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. Supporting Standards: *A1.2.B  Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions and evaluate algebraic expressions that involve variables. *A1.3.C  Evaluate f(x) for a and solve for x in the equation f(x)=b *A1.4.A  Write and solve linear equations and inequalities in one variable A1.5.A  Represent a quadratic function with a symbolic expression, as a graph in a table, and with a description and make connections among the representations. Reasoning, Problem Solving, and Communication Standards: A1.8.E  Read and interpret diagrams, graphs, and text containing the symbols, language and conventions of mathematics.