MO.1.AIII.4 Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
MO.1.AIII.5 Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers; the determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
CS.2.AIII.2 Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant; find the equations for the asymptotes of a hyperbola.
CS.2.AIII.4 Identify, graph, write, and analyze equations of each type of conic section, using properties such as symmetry, intercepts, foci, asymptotes, and eccentricity, and using technology when appropriate.
FOP.3.AIII Students will be able to find the inverse of functions and use composition of functions to prove that two functions are inverses
FOP.3.AIII.1 Compose functions (e.g., if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time).
FOP.3.AIII.4 Produce an invertible function from a non-invertible function by restricting the domain.
FOP.3.AIII.5 Combine standard function types using arithmetic operations (e.g., build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential and relate these functions to the model).
FOP.3.AIII.7 Graph transformations of functions including quadratic, absolute value, square root, cube root, cubic, and step functions; graph piece-wise defined functions including these transformations.
IF.4.AIII.2 Analyze and interpret polynomial functions numerically, graphically, and algebraically, identifying key characteristics such as intercepts, end behavior, domain and range, relative and absolute maximum and minimum, as well as intervals over which the function increases and decreases.
IF.4.AIII.3 Analyze and interpret rational functions numerically, graphically, and algebraically, identifying key characteristics such as asymptotes (vertical, horizontal, and slant), end behavior, point discontinuities, intercepts, and domain and range.
IF.4.AIII.6 Build functions to model real-world applications using algebraic operations on functions and composition of functions, with and without appropriate technology [e.g., profit functions as well as volume and surface area (optimization subject to constraints)].