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Math
Virginia Math
Algebra, Functions, and Data Analysis: Algebra and Functions
Identify graphs and equations of parent functions for linear, quadratic, and exponential function families.
- Compressing functions
- Graphing shifted functions
- Graphs of exponential functions
- Reflect functions
- Reflecting functions introduction
- Reflecting functions: examples
- Scale functions horizontally
- Scale functions vertically
- Scaling functions horizontally: examples
- Scaling functions introduction
- Shift functions
- Shifting functions introduction
- Transforming exponential graphs
- Transforming exponential graphs (example 2)
Describe the transformation from the parent function given the equation or the graph of the function.
- Compressing functions
- Graphing shifted functions
- Graphs of exponential functions
- Reflect functions
- Reflecting functions introduction
- Reflecting functions: examples
- Scale functions horizontally
- Scale functions vertically
- Scaling functions horizontally: examples
- Scaling functions introduction
- Scaling functions vertically: examples
- Shift functions
- Shifting & reflecting functions
- Shifting functions introduction
- Transforming exponential graphs
- Transforming exponential graphs (example 2)
- Transforming functions
Determine and analyze whether a linear, quadratic, or exponential function best models a given representation, including those in context.
Write the equation of a linear, quadratic, or exponential function, given a graph, using transformations of the parent function.
Use a graphical or algebraic representation of a function to solve problems within a context, graphically and algebraically, when appropriate.
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Graph a function given the equation of a function, using transformations of the parent function. Use technology to verify transformations of functions.
Compare and contrast linear, quadratic, and exponential functions using multiple representations (e.g., graphs, tables, equations, verbal descriptions).
- Compare quadratic functions
- Exponential vs. linear models
- Exponential vs. linear models: verbal
- Exponential vs. linear growth
- Exponential vs. linear growth
- Exponential vs. linear growth over time
- Exponential vs. linear growth over time
- Exponential vs. linear models: table
- Linear vs. exponential growth: from data
- Linear vs. exponential growth: from data
- Linear vs. exponential growth: from data (example 2)
- Warmup: exponential vs. linear growth
Determine the domain and range of a function given a graphical representation, including those limited by contexts.
Identify intervals on a graph for which a function is increasing, decreasing, or constant.
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Given a graph, identify the location and value of the absolute maximum and absolute minimum of a function over the domain of a function.
Given a graph, determine the zeros and intercepts of a function.
Describe and recognize the connection between points on the graph and the value of a function.
Describe the end behavior of a function given its graph.
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Identify horizontal and/or vertical asymptotes from the graph of a function, if they exist.
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Describe and relate the characteristics of the graphs of linear, quadratic, exponential, and piecewise-defined functions, including those in contextual situations.
- Exponential decay intro
- Exponential function graph
- Exponential growth vs. decay
- Graphing exponential growth & decay
- Graphing exponential growth & decay
- Graphs of exponential growth
- Graphs of exponential growth
- Interpret a quadratic graph
- Solving equations graphically: word problems
- Two-variable linear equations intro
- Writing exponential functions from graphs
Represent and interpret contextual problems requiring optimization with systems of linear equations or inequalities.
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Solve systems of no more than four equations or inequalities graphically and when appropriate, algebraically.
- Elimination method review (systems of linear equations)
- Equivalent systems of equations review
- Graphing systems of inequalities
- Intro to graphing systems of inequalities
- Systems of equations with elimination
- Systems of equations with elimination challenge
- Systems of equations with elimination: apples and oranges
- Systems of equations with elimination: coffee and croissants
- Systems of equations with elimination: King's cupcakes
- Systems of equations with elimination: potato chips
- Systems of equations with elimination: TV & DVD
- Systems of equations with elimination: x-4y=-18 & -x+3y=11
- Systems of equations with substitution: potato chips
- Systems of equations word problems (with zero and infinite solutions)
- Systems of inequalities word problems
- Why can we subtract one equation from the other in a system of equations?
Identify the feasible region of a system of linear inequalities.
Identify the coordinates of the vertices of a feasible region.
Determine and describe the maximum or minimum value for the function defined over a feasible region.
Interpret the validity of possible solution(s) algebraically, graphically, using technology, and in context and justify the reasonableness of the answer(s) or the solution method in context.
- Solutions of inequalities: graphical
- Solutions of systems of inequalities
- Systems of equations with elimination: apples and oranges
- Systems of equations with elimination: coffee and croissants
- Systems of equations with elimination: TV & DVD
- Systems of equations word problems (with zero and infinite solutions)
- Systems of inequalities word problems
- Testing solutions to systems of inequalities