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.

PC-2.1: Carry out a procedure to graph parent functions (including y = x to the nth power, y = log base a of x, y = ln x, y = 1/x, y = e to the x power, y = a to the x power, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).

Absolute Value with Linear Functions
Arithmetic Sequences
Compound Interest
Exponential Functions
General Form of a Rational Function
Introduction to Exponential Functions
Linear Functions
Logarithmic Functions
Point-Slope Form of a Line
Rational Functions
Slope-Intercept Form of a Line
Standard Form of a Line
Translating and Scaling Functions

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.

Translating and Scaling Sine and Cosine Functions

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.

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Quadratics in Vertex Form
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

PC-2.4: Carry out procedures to algebraically solve equations involving parent functions or transformations of parent functions (including y = x to the nth power, y = log base a of x, y = ln x, y = 1/x, y = e to the x power, y = a to the x power, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).

Exponential Functions

PC-2.5: Analyze graphs, tables, and equations to determine the domain and range of parent functions or transformations of parent functions (including y = x to the nth power, y = log base a of x, y = ln x, y = 1/x, y = e to the x power, y = a to the x power, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).

Exponential Functions
Logarithmic Functions

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.

Polynomials and Linear Factors

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

Function Machines 3 (Functions and Problem Solving)
Logarithmic Functions

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

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

Addition and Subtraction of Functions
Exponential Functions
Graphs of Polynomial Functions
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Polynomial Form
Roots of a Quadratic
Translating and Scaling Functions
Zap It! Game

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

Graphs of Polynomial Functions
Polynomials and Linear Factors
Quadratics in Factored Form

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

General Form of a Rational Function
Rational Functions

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

Polynomials and Linear Factors

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

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

Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

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

Logarithmic Functions

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

Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

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

Logarithmic Functions

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

Exponential Functions
Introduction to Exponential Functions

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

Exponential Functions

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

Exponential Functions

PC-5: The student will demonstrate through the mathematical processes an understanding of the behaviors of trigonometric functions.

PC-5.1: Understand how angles are measured in either degrees or radians.

Triangle Angle Sum

PC-5.2: Carry out a procedure to convert between degree and radian measures.

Cosine Function
Sine Function
Tangent Function

PC-5.4: Carry out a procedure to graph trigonometric functions by analyzing intercepts, periodic behavior, and graphs of reciprocal functions.

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions

PC-5.14: Apply trigonometric relationships (including reciprocal identities; Pythagorean identities; even and odd identities; addition and subtraction formulas of sine, cosine, and tangent; and double angle formulas) to verify other trigonometric identities.

Cosine Function
Simplifying Trigonometric Expressions
Sine Function
Sine, Cosine, and Tangent Ratios
Sum and Difference Identities for Sine and Cosine
Tangent Function

PC-6: The student will demonstrate through the mathematical processes an understanding of the behavior of conic sections both geometrically and algebraically.

PC-6.1: Carry out a procedure to graph the circle whose equation is the form (x-h)² + (y-k)² = r².

Circles

PC-6.2: Analyze given information about the center and the radius or the center and the diameter to write an equation of a circle.

Circles

PC-6.4: Carry out a procedure to graph the ellipse whose equation is the form (((x-h)²)/a²) + (((y-k)²)/b²) = 1.

Ellipses

PC-6.5: Carry out a procedure to graph the hyperbola whose equation is the form (((x-h)²)/a²) - (((y-k)²)/b²) = 1.

Hyperbolas

PC-6.6: Carry out a procedure to graph the parabola whose equation is the form y-k = a(x-h)².

Parabolas