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8.2.1
Understand the concept of function in real-world and mathematical situations, and distinguish between linear and non-linear functions.
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8.2.1.1
Understand that a function is a relationship between an independent variable and a dependent variable in which the value of the independent variable determines the value of the dependent variable. Use functional notation, such as f(x), to represent such relationships.
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8.2.1.2
Use linear functions to represent relationships in which changing the input variable by some amount leads to a change in the output variable that is a constant times that amount.
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8.2.1.3
Understand that a function is linear if it can be expressed in the form f(x)=mx+b or if its graph is a straight line.
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8.2.1.4
Understand that an arithmetic sequence is a linear function that can be expressed in the form f(x)=mx+b, where x = 0, 1, 2, 3,....
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8.2.1.5
Understand that a geometric sequence is a non-linear function that can be expressed in the form f(x)=ab to the x power, where x = 0, 1, 2, 3,....
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8.2.2
Recognize linear functions in real-world and mathematical situations; represent linear functions and other functions with tables, verbal descriptions, symbols and graphs; solve problems involving these functions and explain results in the original context.
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8.2.2.1
Represent linear functions with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another.
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8.2.2.2
Identify graphical properties of linear functions including slopes and intercepts. Know that the slope equals the rate of change, and that the y-intercept is zero when the function represents a proportional relationship.
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8.2.2.3
Identify how coefficient changes in the equation f(x) = mx + b affect the graphs of linear functions. Know how to use graphing technology to examine these effects.
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8.2.2.4
Represent arithmetic sequences using equations, tables, graphs and verbal descriptions, and use them to solve problems.
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8.2.2.5
Represent geometric sequences using equations, tables, graphs and verbal descriptions, and use them to solve problems.
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8.2.3
Generate equivalent numerical and algebraic expressions and use algebraic properties to evaluate expressions.
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8.2.3.1
Evaluate algebraic expressions, including expressions containing radicals and absolute values, at specified values of their variables.
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8.2.3.2
Justify steps in generating equivalent expressions by identifying the properties used, including the properties of algebra. Properties include the associative, commutative and distributive laws, and the order of operations, including grouping symbols.
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8.2.4
Represent real-world and mathematical situations using equations and inequalities involving linear expressions. Solve equations and inequalities symbolically and graphically. Interpret solutions in the original context.
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8.2.4.1
Use linear equations to represent situations involving a constant rate of change, including proportional and non-proportional relationships.
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8.2.4.2
Solve multi-step equations in one variable. Solve for one variable in a multi-variable equation in terms of the other variables. Justify the steps by identifying the properties of equalities used.
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8.2.4.3
Express linear equations in slope-intercept, point-slope and standard forms, and convert between these forms. Given sufficient information, find an equation of a line.
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8.2.4.4
Use linear inequalities to represent relationships in various contexts.
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8.2.4.5
Solve linear inequalities using properties of inequalities. Graph the solutions on a number line.
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8.2.4.6
Represent relationships in various contexts with equations and inequalities involving the absolute value of a linear expression. Solve such equations and inequalities and graph the solutions on a number line.
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8.2.4.7
Represent relationships in various contexts using systems of linear equations. Solve systems of linear equations in two variables symbolically, graphically and numerically.
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8.2.4.8
Understand that a system of linear equations may have no solution, one solution, or an infinite number of solutions. Relate the number of solutions to pairs of lines that are intersecting, parallel or identical. Check whether a pair of numbers satisfies a system of two linear equations in two unknowns by substituting the numbers into both equations.
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8.2.4.9
Use the relationship between square roots and squares of a number to solve problems.
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IXL Learning. All rights reserved.