### 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

Correlation last revised: 5/24/2018