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Math
Virginia Math
Mathematical Analysis: Functional Relationships
Construct the composition of functions algebraically and graphically.
Determine the domain and range of composite functions algebraically and graphically.
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Develop the inverse of a function algebraically and graphically.
- Evaluate inverse functions
- Find inverses of rational functions
- Finding inverse functions: rational
- Graphing the inverse of a linear function
- Graphs of logarithms & exponentials
- Inputs & outputs of inverse functions
- Intro to arccosine
- Intro to arcsine
- Intro to arctangent
- Intro to inverse functions
- Intro to inverse functions
- Relationship between exponentials & logarithms
- Relationship between exponentials & logarithms: graphs
Compare the domain and range of the inverse of a function with the original function, both algebraically and graphically.
Use mathematical reasoning to generalize and communicate the criteria for an inverse function to exist.
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Generalize characteristics of exponential and logarithmic functions from an equation or a graph.
- Exponential expressions word problems (algebraic)
- Exponential expressions word problems (algebraic)
- Exponential growth vs. decay
- Graphs of logarithms & exponentials
- Interpret exponential expressions word problems
- Interpreting exponential expression word problem
- Relationship between exponentials & logarithms
- Relationship between exponentials & logarithms: graphs
Define 𝑒 and estimate its value.
Convert between equations written in logarithmic and exponential form.
- Evaluate logarithms
- Evaluate logarithms (advanced)
- Evaluating logarithms (advanced)
- Evaluating logarithms: change of base rule
- Evaluating natural logarithm with calculator
- Intro to logarithm properties
- Intro to logarithm properties (1 of 2)
- Intro to logarithm properties (2 of 2)
- Intro to logarithms
- Intro to Logarithms
- Logarithm change of base rule intro
- Proof of the logarithm product rule
- Proof of the logarithm quotient and power rules
- Relationship between exponentials & logarithms
- Relationship between exponentials & logarithms
- Relationship between exponentials & logarithms: tables
- Solve exponential equations using logarithms: base-10 and base-e
- Solve exponential equations using logarithms: base-2 and other bases
- Solving exponential equations using logarithms
- Solving exponential equations using logarithms: base-10
- Solving exponential equations using logarithms: base-2
- Using the logarithm change of base rule
- Using the logarithmic power rule
- Using the logarithmic product rule
- Using the properties of logarithms: multiple steps
Use laws of exponents and properties of logarithms to solve equations and simplify expressions.
- Equivalent forms of exponential expressions
- Equivalent forms of exponential expressions
- Evaluate logarithms
- Evaluate logarithms (advanced)
- Evaluate logarithms: change of base rule
- Evaluating fractional exponents
- Evaluating fractional exponents: fractional base
- Evaluating fractional exponents: negative unit-fraction
- Evaluating logarithms (advanced)
- Evaluating logarithms: change of base rule
- Evaluating quotient of fractional exponents
- Exponential equation with rational answer
- Exponential equation word problem
- Fractional exponents
- Graphs of logarithms & exponentials
- Intro to logarithm properties
- Intro to logarithm properties (1 of 2)
- Intro to logarithm properties (2 of 2)
- Intro to Logarithms
- Intro to rational exponents
- Logarithm change of base rule intro
- Proof of the logarithm product rule
- Proof of the logarithm quotient and power rules
- Properties of exponents (rational exponents)
- Properties of exponents (rational exponents)
- Rational exponents challenge
- Relationship between exponentials & logarithms
- Relationship between exponentials & logarithms: graphs
- Relationship between exponentials & logarithms: tables
- Rewrite exponential expressions
- Rewriting quotient of powers (rational exponents)
- Rewriting roots as rational exponents
- Simplifying exponential expressions
- Solve exponential equations using exponent properties
- Solve exponential equations using exponent properties (advanced)
- Solve exponential equations using logarithms: base-10 and base-e
- Solve exponential equations using logarithms: base-2 and other bases
- Solving exponential equations using exponent properties
- Solving exponential equations using exponent properties (advanced)
- Solving exponential equations using logarithms
- Solving exponential equations using logarithms: base-10
- Solving exponential equations using logarithms: base-2
- Unit-fraction exponents
- Use the logarithm change of base rule
- Use the properties of logarithms
- Using the logarithm change of base rule
- Using the logarithmic power rule
- Using the logarithmic product rule
- Using the properties of logarithms: multiple steps
Represent contextual problems, using exponential and logarithmic functions, to include common and natural logarithms.
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Sketch the graph of exponential and logarithmic functions and identify asymptotes, end behavior, intercepts, domain, and range.
Use and interpret the notation: ∑, 𝑛, 𝑛ᵗʰ, and 𝑎ₙ.
- Arithmetic series
- Arithmetic series worksheet
- Finite geometric series
- Geometric series intro
- Geometric series with sigma notation
- Intro to arithmetic sequences
- Intro to geometric sequences
- Sequences intro
- Summation notation
- Summation notation intro
- Worked example: arithmetic series (sigma notation)
- Worked example: finite geometric series (sigma notation)
Derive the formulas associated with arithmetic and geometric sequences and series.
- Arithmetic series formula
- Arithmetic series intro
- Converting recursive & explicit forms of arithmetic sequences
- Converting recursive & explicit forms of arithmetic sequences
- Converting recursive & explicit forms of arithmetic sequences
- Converting recursive & explicit forms of geometric sequences
- Converting recursive & explicit forms of geometric sequences
- Explicit & recursive formulas for geometric sequences
- Explicit formulas for arithmetic sequences
- Explicit formulas for arithmetic sequences
- Explicit formulas for geometric sequences
- Finite geometric series
- Finite geometric series formula justification
- Finite geometric series word problem: social media
- Geometric sequences review
- Geometric series intro
- Intro to arithmetic sequence formulas
- Intro to geometric sequences
- Proof of finite arithmetic series formula
- Recursive formulas for arithmetic sequences
- Recursive formulas for arithmetic sequences
- Recursive formulas for geometric sequences
- Sequences intro
- Sequences word problems
- Sequences word problems
- Using recursive formulas of geometric sequences
Determine the 𝑛ᵗʰ term, 𝑎ₙ, for an arithmetic or geometric sequence.
- Arithmetic sequence problem
- Arithmetic series formula
- Arithmetic series intro
- Evaluate sequences in recursive form
- Evaluating sequences in recursive form
- Geometric series formula
- Geometric series word problems: hike
- Use arithmetic sequence formulas
- Use geometric sequence formulas
- Using explicit formulas of geometric sequences
- Using recursive formulas of geometric sequences
- Worked example: using recursive formula for arithmetic sequence
Determine the sum, 𝑆ₙ, if it exists, of an arithmetic or geometric series.
- Arithmetic series
- Arithmetic series
- Arithmetic series worksheet
- Finite geometric series
- Finite geometric series word problem: mortgage
- Finite geometric series word problems
- Geometric series formula
- Geometric series intro
- Geometric series introduction
- Geometric series word problems: swing
- Proof of finite arithmetic series formula
- Worked example: arithmetic series (recursive formula)
- Worked example: arithmetic series (sigma notation)
- Worked example: arithmetic series (sum expression)
- Worked example: finite geometric series (sigma notation)
- Worked examples: finite geometric series
Model and solve problems in context, using sequences and series.
Distinguish between a convergent and divergent series.
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Describe convergent series in relation to the concept of a limit.
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