110-1 Concept of Function
Students will be able to…
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Identify if a relationship is a function and justify with the definition of a function.
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Demonstrate proper use of function notation.
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Given any of the four representations of a function, (algebraic, table, graph, contextual), students will be able to …
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Identify independent and dependent variables.
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Identify domain and range using interval or inequality notation.
**for all functions not listed in 110-2
110-2 Families of Functions
Students will be able to identify, solve for, and/or interpret the characteristics of each family of functions as appropriate (linear(L), exponential(E), logarithmic(G), power(P), polynomial(Y), quadratic(Q)):
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Intercepts
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Rates of Change
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Asymptotes
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End Behavior
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Domain and Range (using interval or inequality notation).
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Maximum and Minimum
Given any of the four representations of a function, students will be able to …
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Identify the function family
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Match to an equivalent representation
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Create an equivalent representation
Students will be able to write the equation for
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A linear function (from the vertical intercept and a rate OR from two points)
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A piecewise function (from a table, graph or context)
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An exponential function (from the vertical intercept and a rate, from the vertical intercept and another point, or from financial information)
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A power function (from context)
Given any of the four representation of a function, students will be able to identify and apply simple transformations:
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Horizontal/vertical shifts
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Horizontal/vertical axis reflections
110-3 Modeling with technology
Given data, students will be able to …
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Identify the most appropriate model based both on technology and the context of the situation and justify reasoning.
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Use technology (regression) to find a curve of best fit.
110-4 Algebraic Manipulation
Students will be able to perform the following manipulative skills and interpret the results:
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Given input, find output.
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Given output, find input.
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Students will be able to perform the following manipulative skills with algebraic expressions and equations:
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Use the rules of integer and rational exponents to simplify simple expressions.
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Rewrite a logarithmic equation into exponential form and vice versa.
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Factor simple equations.
110-5 Systems
Given a system of linear equations…
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Write equations for the system (in standard or slope-intercept form).
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Solve and interpret the results of a system of equations both graphically and algebraically.
Given a system of inequalities…
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Write the system of inequalities.
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Solve the system graphically.
110-6 Composition and Inverses
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Perform a composition of two functions both with specific numbers and with variables.
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Find the inverse of a given function using proper inverse function notation.
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Given a context and a function such as t-1(4)=20, a student will be able to interpret the equation in context.
110-7 General Mathematical Skills
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Explain complex mathematical concepts and procedures using appropriate mathematical terminology.
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Organize and update a math portfolio as directed in a portfolio.