Unit Titles |
Unit 1: Families of Functions
Unit 2: Systems of Linear Equations and Inequalities
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Unit 3: Introduction to Quadratic Functions
Unit 4: Applications of Quadratic Functions
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Unit 5: Polynomial and Radical Functions
Unit 6: Exponential Functions
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Unit 7: Rational Equations and Functions
Unit 8: Trigonometry and Probability
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Learning Outcomes
(grade level expectations or standards)
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- Identify and sketch the graph of the parent functions
- Determine the domain and range of each parent function
- Describe the effect of horizontal and vertical phase shifts
- Describe the effect of the lead coefficient on the graph
- Given the parent function, apply given transformations
- Given the transformation, determine the representative equation
- Determine the zeros of functions and describe how they relate to equations
- Solve absolute value equations
- Graphs piecewise, absolute value and greatest integer functions
- Identify intervals of increasing, decreasing, constant, concave up and concave down
- Solve all systems of linear equations graphically, algebraically, and with matrices
- Graph linear inequalities
- Describe the number of solutions to a systems problem as unique, infinite, or nonexistent
- Calculate and graph the inverse of linear functions
- Solve systems of linear inequalities algebraically and graphically
- Solve linear programming problems
- Model and solve other real life problems with more than one variable
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- Define quadratic functions
- Graph quadratic functions manually and with technology
- Identify domain and range of quadratic functions
- Completely analyze the graph of a quadratic function with regards to domain and range; x and y intercepts; vertex; line of symmetry; intervals of increasing and decreasing; and concavity
- Solve quadratic equations using factoring, completing the square, quadratic formula, and graphically
- Derive the quadratic formula by completing the square
- Calculate the descriminant and use descriminant to describe roots
- Define the family of complex numbers
- Perform operations on complex numbers
- Identify complex roots of quadratic functions
- Solve and graph quadratic inequalities
- Write quadratic functions in standard, intercept and vertex forms
- Graph quadratic functions and describe from parent functions
- Identify a quadratic function from its graph
- Model real world data with quadratic functions
- Solve real world problems that can be modeled with quadratic functions, included, but limited to profit, velocity, area
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- Define a polynomial function
- Completely analyze the graph of a polynomial function with regards to domain, range, x and y intercepts, zero’s, intervals of increasing and decreasing, concavity
- Find zero’s of a polynomial function algebraically
- Solve polynomial equations graphically and algebraically
- Perform operations with polynomials
- Perform transformations on the graphs of polynomial functions and identify the new function
- Model data with polynomial functions
- Solve real world problems that can be modeled with polynomial functions
- Define a radical function
- Completely analyze the graph of a radical function with regards to domain, range, x and y intercepts, zero’s, intervals of increasing and decreasing, concavity
- Find zero’s of a radical function algebraically
- Perform transformations on the graphs of radical functions and identify the new function
- Solve radical equations graphically and algebraically
- Perform operations with radicals
- Model data with radical functions
- Solve real world problems that can be modeled with radical functions
- Define an exponential function
- Completely analyze the graph of a exponential function with regards to domain, range, x and y intercepts, zero’s, intervals of increasing and decreasing, concavity
- Find zero’s of an exponential function algebraically
- Perform transformations on the graphs of exponential functions and identify the new function
- Calculate and graph the inverse of exponential functions
- Solve exponential equations graphically and algebraically
- Model data with exponential functions
- Solve real world problems that can be modeled with exponential functions
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- Define a rational function
- Completely analyze the graph of a rational function with regards to domain, range, x and y intercepts, zero’s, intervals of increasing and decreasing, concavity
- Find zero’s of a rational function algebraically
- Perform transformations on the graphs of rational functions and identify the new function
- Solve rational equations graphically and algebraically
- Model data with rational functions
- Solve real world problems that can be modeled with rational functions
- Develop trigonometric ratios from the right triangles
- Solve problems using trigonometric ratios (distance, angle of elevation)
- Analyze the graphs of the trigonometric functions
- Convert angle measures (degrees to radians, radians to degrees)
- Express trig ratios in both radians and degrees
- Graph the trigonometric functions (sin x, cos x & tan x)
- Use the Pythagorean theorem to develop the trigonometric identities
- Identify and apply trigonometric identities
- Identify and apply the inverse trigonometric identities
- Use the trigonometric identities to solve real world problems
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Significant Task
(names only)
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Linear Systems: Using Graphs and Tables
Linear Systems: Using Algebra
Maximizing Your Efforts
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Exploring the Vertex Form of the Quadratic Function
Rocket Science
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Exploring the Exponential Function |
Math TODAY: Humidity Makes Air Feel Hotter III
Hurricane Hunters: Tracking Katrina and Rita
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Content
Supporting Materials
(text, calcs, manips)
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Text
Visual Aids
Graphing Calculators
Graph paper
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Text
Visual Aids
Graphing Calculators
Graph paper
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Text
Visual Aids
Graphing Calculators
Graph paper
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Text
Visual Aids
Graphing Calculators
Graph paper
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