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Standard PC-1:   The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

Indicators

PC-1.1     Communicate knowledge of algebraic and trigonometric relationships by using mathematical terminology appropriately.

PC-1.2     Connect algebra and trigonometry with other branches of mathematics.

PC-1.3     Apply algebraic methods to solve problems in real-world contexts.

PC-1.4     Judge the reasonableness of mathematical solutions.

PC-1.5     Demonstrate an understanding of algebraic and trigonometric relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic).

PC-1.6     Understand how algebraic and trigonometric relationships can be represented in concrete models, pictorial models, and diagrams.

PC-1.7     Understand how to represent algebraic and trigonometric relationships by using tools such as handheld computing devices, spreadsheets, and computer algebra systems (CASs).

Standard PC-2:    The student will demonstrate through the mathematical processes an understanding of the characteristics and behaviors of functions and the effect of operations on functions.

Indicators

PC-2.1       Carry out a procedure to graph parent functions (including y = xⁿ, y = log_a x, y = ln x, y = , y = e^x, y = a^x, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).

PC-2.2       Carry out a procedure to graph transformations (including –f(x), a • f(x), f(x) + d,

                  f(x - c), f(-x), f(b • x), |f(x)|, and f(|x|)) of parent functions and combinations of transformations.

PC-2.3       Analyze a graph to describe the transformation (including –f(x), a • f(x), f(x) + d,

                  f(x - c), f(-x), f(b • x), |f(x)|, and f(|x|)) of parent functions.

PC-2.4       Carry out procedures to algebraically solve equations involving parent functions or transformations of parent functions (including y = xⁿ, y = log_a x, y = ln x, y = ,

                  y = e^x, y = a^x, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).

PC-2.5       Analyze graphs, tables, and equations to determine the domain and range of parent functions or transformations of parent functions (including y = xⁿ, y = log_a x, y = ln x, y = , y = e^x, y = a^x, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).

PC-2.6       Analyze a function or the symmetry of its graph to determine whether the function is even, odd, or neither.

PC-2.7       Recognize and use connections among significant points of a function (including roots, maximum points, and minimum points), the graph of a function, and the algebraic representation of a function.

PC-2.8       Carry out a procedure to determine whether the inverse of a function exists.

PC-2.9       Carry out a procedure to write a rule for the inverse of a function, if it exists.

Standard PC-3:    The student will demonstrate through the mathematical processes an understanding of the behaviors of polynomial and rational functions.

Indicators

PC-3.1       Carry out a procedure to graph quadratic and higher-order polynomial functions by analyzing intercepts and end behavior.

PC-3.2       Apply the rational root theorem to determine a set of possible rational roots of a polynomial equation.

PC-3.3       Carry out a procedure to calculate the zeros of polynomial functions when given a set of possible zeros.

PC-3.4       Carry out procedures to determine characteristics of rational functions (including domain, range, intercepts, asymptotes, and discontinuities).

PC-3.5       Analyze given information to write a polynomial function that models a given problem situation.

PC-3.6       Carry out a procedure to solve polynomial equations algebraically.

PC-3.7       Carry out a procedure to solve polynomial equations graphically.

PC-3.8       Carry out a procedure to solve rational equations algebraically. 

PC-3.9       Carry out a procedure to solve rational equations graphically.

PC-3.10     Carry out a procedure to solve polynomial inequalities algebraically.

PC-3.11     Carry out a procedure to solve polynomial inequalities graphically.

Standard PC-4:      The student will demonstrate through the mathematical processes an understanding of the behaviors of exponential and logarithmic functions.

Indicators

PC-4.1       Carry out a procedure to graph exponential functions by analyzing intercepts and end behavior.

PC-4.2       Carry out a procedure to graph logarithmic functions by analyzing intercepts and end behavior.

PC-4.3       Carry out procedures to determine characteristics of exponential functions (including domain, range, intercepts, and asymptotes).

PC-4.4       Carry out procedures to determine characteristics of logarithmic functions (including domain, range, intercepts, and asymptotes).

PC-4.5       Apply the laws of exponents to solve problems involving rational exponents.

PC-4.6       Analyze given information to write an exponential function that models a given problem situation.

PC-4.7       Apply the laws of logarithms to solve problems.

PC-4.8       Carry out a procedure to solve exponential equations algebraically.

PC-4.9       Carry out a procedure to solve exponential equations graphically.

PC-4.10     Carry out a procedure to solve logarithmic equations algebraically.

PC-4.11     Carry out a procedure to solve logarithmic equations graphically.