Students explore, describe, and analyze the attributes of functions. Students make connections between multiple representations of functions and algebraically construct new functions. Students analyze and use functions to model real-world problems.
- Use the composition of two functions to model and solve real-world problems
- Demonstrate that function composition is not always commutative
- Graph piecewise-defined functions, including step functions
Relations and Geometric Reasoning
Students model and make connections between algebraic and geometric relations.
- Graph a set of parametric equations
- Graph points in the polar coordinate system and convert between rectangular coordinates and polar coordinates
- Graph polar equations by plotting points and using technology
- Determine the conic section formed when a plane intersects a double-napped cone
- Make connections between the locus definition of conic sections and their equations in rectangular coordinates
- Use the characteristics of an ellipse to write the equation of an ellipse
- Use the characteristics of a hyperbola to write the equation of a hyperbola
Number and Measure
Students apply appropriate techniques, tools, and formulas to calculate measures in mathematical and real-world problems.
- Represent the addition of vectors and the multiplication of a vector by a scalar geometrically and symbolically
Students evaluate expressions, describe patterns, formulate models, and solve equations and inequalities using properties, procedures, or algorithms.
- Generate and solve logarithmic equations in mathematical and real-world problems
- Generate and solve exponential equations in mathematical and real-world problems
- Solve polynomial equations in mathematical and real-world problems
- Solve polynomial inequalities and write the solutions set in interval notation
- Solve rational inequalities and write the solution set in interval notation