Main content
Math
- 6.2: Number and operations
- 6.3: Number and operations
- 6.4: Proportionality
- 6.5: Proportionality
- 6.6: Expressions, equations, and relationships
- 6.7: Expressions, equations, and relationships
- 6.8: Expressions, equations, and relationships
- 6.9: Expressions, equations, and relationships
- 6.10: Expressions, equations, and relationships
- 6.11: Measurement and data
- 6.12: Measurement and data
- 6.13: Measurement and data
- 6.14: Personal financial literacy
- 7.2: Numbers and operations
- 7.3: Number and operations
- 7.4: Proportionality
- 7.5: Proportionality
- 7.6: Proportionality
- 7.7: Expressions, equations, and relationships
- 7.8: Expressions, equations, and relationships
- 7.9: Expressions, equations, and relationships
- 7.10: Expressions, equations, and relationships
- 7.11: Expressions, equations, and relationships
- 7.12: Measurement and data
- 7.13: Personal financial literacy
- 8.2: Number and operations
- 8.3: Proportionality
- 8.4: Proportionality
- 8.5: Proportionality
- 8.6: Expressions, equations, and relationships
- 8.7: Expressions, equations, and relationships
- 8.8: Expressions, equations, and relationships
- 8.9: Expressions, equations, and relationships
- 8.10: Two-dimensional shapes
- 8.11: Measurement and data
- 8.12: Personal financial literacy
- A.2: Linear functions, equations, and inequalities
- A.3: Linear functions, equations, and inequalities
- A.4: Linear functions, equations, and inequalities
- A.5: Linear functions, equations, and inequalities
- A.6: Quadratic functions and equations
- A.7: Quadratic functions and equations
- A.8: Quadratic functions and equations
- A.9: Exponential functions and equations
- A.10: Number and algebraic methods
- A.11: Number and algebraic methods
- A.12: Number and algebraic methods
- A2.2: Attributes of functions and their inverses
- A2.3: Systems of equations and inequalities
- A2.4: Quadratic and square root functions, equations, and inequalities
- A2.5: Exponential and logarithmic functions and equations
- A2.6: Cubic, cube root, absolute value and rational functions, equations, and inequalities
- A2.7: Number and algebraic methods
- A2.8: Data
- G.2: Coordinate and transformational geometry
- G.3: Coordinate and transformational geometry
- G.4: Logical argument and constructions
- G.5: Logical argument and constructions
- G.6: Proof and congruence
- G.7: Similarity, proof, and trigonometry
- G.8: Similarity, proof, and trigonometry
- G.9: Similarity, proof, and trigonometry
- G.10: Two-dimensional and three-dimensional figures
- G.11: Two-dimensional and three-dimensional figures
- G.12: Circles
- G.13: Probability
- MMA.2: Mathematical modeling in personal finance
- MMA.3: Mathematical modeling in personal finance
- MMA.4: Mathematical modeling in personal finance
- MMA.5: Mathematical modeling in science and engineering
- MMA.6: Mathematical modeling in science and engineering
- MMA.7: Mathematical modeling in fine arts
- MMA.8: Mathematical modeling in social sciences
- MMA.9: Mathematical modeling in social sciences
- MMA.10: Mathematical modeling in social sciences
Texas Math
Precalculus: Functions. The student uses process standards in mathematics to explore, describe, and analyze the attributes of functions. The student makes connections between multiple representations of functions and algebraically constructs new functions. The student analyzes and uses functions to model real-world problems.
Use the composition of two functions to model and solve real-world problems.
- Composing functions
- Evaluating composite functions
- Evaluating composite functions (advanced)
- Evaluating composite functions: using tables
- Intro to composing functions
- Meaningfully composing functions
- Model with composite functions
- Modeling with composite functions
- Modeling with composite functions: skydiving
Demonstrate that function composition is not always commutative.
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Represent a given function as a composite function of two or more functions.
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Describe symmetry of graphs of even and odd functions.
Determine an inverse function, when it exists, for a given function over its domain or a subset of its domain and represent the inverse using multiple representations.
- Domain & range of inverse tangent function
- Find inverses of rational functions
- Finding inverses of rational functions
- Inverse functions: graphs and tables
- Reading inverse values from a graph
- Reading inverse values from a table
- Restrict domains of functions to make them invertible
- Restricting domains of functions to make them invertible
Graph exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions.
- Amplitude & period of sinusoidal functions from equation
- Example: Graphing y=-cos(π⋅x)+1.5
- Example: Graphing y=3⋅sin(½⋅x)-2
- Finding average rate of change of polynomials
- Graph of y=tan(x)
- Graph sinusoidal functions
- Graph sinusoidal functions: phase shift
- Graphing exponential functions
- Graphs of exponential functions
- Graphs of polynomials
- Graphs of polynomials: Challenge problems
- Intersection points of y=sin(x) and y=cos(x)
- Sign of average rate of change of polynomials
- Transforming sinusoidal graphs: vertical & horizontal stretches
- Transforming sinusoidal graphs: vertical stretch & horizontal reflection
Graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and their transformations, including af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d, in mathematical and real-world problems.
- End behavior of rational functions
- Graphing logarithmic functions (example 1)
- Graphing logarithmic functions (example 2)
- Graphing rational functions according to asymptotes
- Graphs of exponential functions
- Graphs of logarithmic functions
- Graphs of rational functions
- Graphs of rational functions: vertical asymptotes
- Graphs of rational functions: y-intercept
- Graphs of rational functions: zeros
- Reflect functions
- Reflecting functions introduction
- Reflecting functions: examples
- Transforming exponential graphs
- Transforming exponential graphs (example 2)
- Transforming sinusoidal graphs: vertical & horizontal stretches
- Transforming sinusoidal graphs: vertical stretch & horizontal reflection
- Trig word problem: solving for temperature
Graph arc sin x and arc cos x and describe the limitations on the domain.
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Determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing.
- Amplitude & period of sinusoidal functions from equation
- Amplitude of sinusoidal functions from equation
- Amplitude of sinusoidal functions from graph
- Average rate of change of polynomials
- Construct sinusoidal functions
- Discontinuities of rational functions
- End behavior of rational functions
- Example: Graphing y=-cos(π⋅x)+1.5
- Example: Graphing y=3⋅sin(½⋅x)-2
- Features of sinusoidal functions
- Finding average rate of change of polynomials
- Graph sinusoidal functions
- Graph sinusoidal functions: phase shift
- Graphing exponential functions
- Graphing rational functions according to asymptotes
- Graphs of exponential functions
- Graphs of rational functions
- Graphs of rational functions: horizontal asymptote
- Graphs of rational functions: vertical asymptotes
- Graphs of rational functions: y-intercept
- Graphs of rational functions: zeros
- Interpreting trigonometric graphs in context
- Interpreting trigonometric graphs in context
- Intersection points of y=sin(x) and y=cos(x)
- Intro to arccosine
- Intro to arcsine
- Intro to arctangent
- Midline of sinusoidal functions from equation
- Midline of sinusoidal functions from graph
- Midline, amplitude, and period review
- Multiplicity of zeros of polynomials
- Period of sinusoidal functions from equation
- Period of sinusoidal functions from graph
- Periodicity of algebraic models
- Periodicity of algebraic models
- Positive & negative intervals of polynomials
- Positive & negative intervals of polynomials
- Positive and negative intervals of polynomials
- Rational functions: zeros, asymptotes, and undefined points
- Sign of average rate of change of polynomials
- Sine & cosine identities: symmetry
- Sinusoidal function from graph
- Solving equations graphically: word problems
- Tangent identities: symmetry
- Transforming sinusoidal graphs: vertical & horizontal stretches
- Transforming sinusoidal graphs: vertical stretch & horizontal reflection
- Zeros of polynomials (factored form)
- Zeros of polynomials (multiplicity)
- Zeros of polynomials (multiplicity)
- Zeros of polynomials (with factoring)
- Zeros of polynomials (with factoring): common factor
- Zeros of polynomials (with factoring): grouping
- Zeros of polynomials & their graphs
- Zeros of polynomials introduction
- Zeros of polynomials: matching equation to graph
- Zeros of polynomials: matching equation to zeros
- Zeros of polynomials: plotting zeros
Analyze and describe end behavior of functions, including exponential, logarithmic, rational, polynomial, and power functions, using infinity notation to communicate this characteristic in mathematical and real-world problems.
Analyze characteristics of rational functions and the behavior of the function around the asymptotes, including horizontal, vertical, and oblique asymptotes.
- Discontinuities of rational functions
- End behavior of rational functions
- Graphing rational functions according to asymptotes
- Graphs of rational functions
- Graphs of rational functions: horizontal asymptote
- Graphs of rational functions: vertical asymptotes
- Graphs of rational functions: y-intercept
- Graphs of rational functions: zeros
- Infinite limits and asymptotes
- Rational functions: zeros, asymptotes, and undefined points
Determine various types of discontinuities in the interval (-∞, ∞) as they relate to functions and explore the limitations of the graphing calculator as it relates to the behavior of the function around discontinuities;
Describe the left-sided behavior and the right-sided behavior of the graph of a function around discontinuities.
Analyze situations modeled by functions, including exponential, logarithmic, rational, polynomial, and power functions, to solve real-world problems.
- Average rate of change of polynomials
- Constructing exponential models: percent change
- Finding average rate of change of polynomials
- Interpret change in exponential models: changing units
- Interpret change in exponential models: with manipulation
- Interpreting change in exponential models
- Interpreting change in exponential models: with manipulation
- Interpreting time in exponential models
- Sign of average rate of change of polynomials
- Solving equations by graphing
- Solving equations by graphing: graphing calculator
- Solving equations by graphing: word problems
- Solving equations graphically: graphing calculator
- Solving equations graphically: intro
- Solving equations graphically: word problems
Develop and use a sinusoidal function that models a situation in mathematical and real-world problems.
Determine the values of the trigonometric functions at the special angles and relate them in mathematical and real-world problems.