Skip to main content
\(\require{\require{color,soul}}\newcommand{\abs}[1]{\left\lvert#1\right\rvert} \newcommand{\point}[2]{\left(#1,#2\right)} \newcommand{\highlight}[1]{{\color{blue}{{#1}}}} \newcommand{\highlightr}[1]{{\color{red}{{#1}}}} \newcommand{\highlightg}[1]{{\color{green}{{#1}}}} \newcommand{\highlightp}[1]{{\color{purple}{{#1}}}} \newcommand{\highlightb}[1]{{\color{brown}{{#1}}}} \newcommand{\highlighty}[1]{{\color{gray}{{#1}}}} \newcommand{\lowlight}[1]{{\color{lightgray}{#1}}} \newcommand{\attention}[1]{\mathord{\overset{\downarrow}{#1}}} \newcommand{\substitute}[1]{{\color{blue}{{#1}}}} \newcommand{\addright}[1]{{\color{blue}{{{}+#1}}}} \newcommand{\addleft}[1]{{\color{blue}{{#1+{}}}}} \newcommand{\subtractright}[1]{{\color{blue}{{{}-#1}}}} \newcommand{\multiplyright}[2][\cdot]{{\color{blue}{{{}#1#2}}}} \newcommand{\multiplyleft}[2][\cdot]{{\color{blue}{{#2#1{}}}}} \newcommand{\divideunder}[2]{\frac{#1}{{\color{blue}{{#2}}}}} \newcommand{\divideright}[1]{{\color{blue}{{{}\div#1}}}} \newcommand{\apple}{\text{🍎}} \newcommand{\banana}{\text{🍌}} \newcommand{\pear}{\text{🍐}} \newcommand{\cat}{\text{🐱}} \newcommand{\dog}{\text{🐶}} \newcommand{\uvec}[1]{\boldsymbol{\hat{\textbf{#1}}}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \)
PCC SLC Math Resources
Portland Community College Mathematics Faculty
Contents
Calc
Prev
Up
Next
Contents
Prev
Up
Next
Front Matter
Colophon
Acknowledgements
About This Site
1
Material Sorted by PCC Course Numbers
Topics Covered in MTH 60
Topics Covered in MTH 65
Topics Covered in MTH 95
Topics Covered in MTH 111
Topics Covered in MTH 112
2
Absolute Value
Videos Created by Emily Nelson
Basic Absolute Value Equations
Basic Absolute Inequalities
Isolating the Absolute Value Expression
Additional Practice Solving Absolute Value Equations and Inequalities
3
Exponents and Scientific Notation
Videos Created by Ann Cary and Scot Leavitt
Properties of Exponents
Negative Exponents
Summary of the Rules of Exponents
Scientific Notation
Additional Practice with Exponents and Scientific Notation
4
Factoring
Videos Created by Ann Cary and Scot Leavitt
Factoring the Greatest Common Factor
Factoring Trinomials with Leading Coefficients of 1
Factoring by Grouping
Factoring Trinomials with Leading Coefficients not 1
Factoring Binomials
Factoring: A General Strategy
Additional Practice Factoring
5
Functions
Videos Created by Emily Nelson
Videos Created by Ann Cary
Introduction to Function Notation
Domain and Range of Functions
Advanced Function Notation
Graphical Transformations
Even Functions and Odd Functions
Difference Quotients
Function Composition
Inverse Functions
Using Function Graphs to Determine Solution Sets to Inequalities
Additional Practice Related to Functions
6
Imaginary and Complex Numbers
Videos Created by Emily Nelson
Imaginary Numbers
Complex Numbers
Additional Practice Related to Imaginary and Complex Numbers
7
Lines
Videos Created by Ann Cary and Scot Leavitt
Intercepts and the Standard Form of the Equation of a Line
Slope of a Line
The Slope-Intercept Form of the Equation of a Line
The Point-Slope Form of the Equation of a Line
Parallel Lines, Perpendicular Lines, Horizontal and Vertical Lines
Additional Practice Related to Lines
8
Linear Equations and Linear Inequalities in One Variable
Introduction to Linear Equations in One Variable
Linear Equations in One Variable - Part II
Literal Equations
Linear Inequalities in One Variable
9
Logarithmic and Exponential Functions
Videos Created by Ann Cary
Exponential Functions and Their Graphs
Logarithmic Functions and Their Graphs
Logarithms as Exponents
Derivations of the Properties of Logarithms
Applying the Properties of Logarithms
Logarithmic Equations
Exponential Equations
The Number \(e\)
Exponential Growth and Decay
Additional Practice Related to Logarithms and Exponential Equations
10
Parabolas
Videos Created by Ann Cary and Scot Leavitt
Videos Created by Emily Nelson
Standard Form
Vertex Form
Completing the Square
Additional Practice Related to Parabolas
11
Polynomials
Videos Created by Ann Cary and Scot Leavitt
Polynomial Terminology
Addition and Subtraction of Polynomials
Multiplication of Polynomials
Division of Polynomials by Monomials
Additional Practice Related to Polynomials
12
Quadratic Equations
Videos Created by Ann Cary and Scot Leavitt
Videos Created by Emily Nelson
Solving Quadratic Equations Using the Zero-Product Property
Solving Quadratic Equations by the Square Root Method
Solving Quadratic Equations by Completing the Square
Derivation of the Quadratic Formula
Applying the Quadratic Formula
Complex Number Solutions to Quadratic Equations
The Discriminant
Applications of Quadratic Equations
Additional Practice with Quadratic Equations
13
Radicals and Rational Exponents
Videos Created by Ann Cary and Scot Leavitt
Videos Created by Emily Nelson
Simplifying Square Root Expressions
Rationalizing Monomial Square Root Denominators
Adding and Subtracting Square Root Expressions
Rationalizing Binomial-Denominators that include Square Root expressions
Radicals with Indices Greater than Two
Rational Exponents
Equations Containing Radical Expressions
Additional Practice with Radicals and Rational Exponents
14
Rational Expressions, Equations, Functions, and Graphs
Videos Created by Emily Nelson
Videos Created by Ann Cary
Domains of Rational Functions
Simplifying Rational Expressions
Multiplication and Division of Rational Expressions
Addition and Subtraction of Rational Expressions
Complex Fractions
Rational Equations
Rational Functions and Their Graphs
Applications of Rational Equations
Additional Practice Related to Rational Expressions and Rational Equations
15
Systems of Linear Equations
Videos Created by Ann Cary and Scot Leavitt
Graphing Systems of Linear Equations
Solving Systems Using the Substitution Method
Solving Systems Using the Elimination Method
Applications of Systems of Linear Equations
Additional Practice Related to Systems of Linear Equations
16
Trigonometry
The Unit Circle/Angles in Standard Position/Arc Length
The Six Basic Trigonometric Functions
Special Angles/Reference Angles
The Graphs of the Sine and Cosine Functions
The Graphs of the Tangent and Cotangent Functions
The Graphs of the Secant and Cosecant Functions
The Fundamental Trigonometric Identities
Multi-Angle Identities
Additional Trigonometric Identities
Trigonometric Equations
The Inverse Trigonometric Functions
Right Triangle Trigonometry
The Law of Sines and The Law of Cosines
Polar Coordinates
Complex Numbers/de Moivre's Theorem/Euler's Formula
Vectors in 2-Dimensions
17
GeoGebra Applets
GeoGebra Applets Master List
Determine the Intercepts of a Line Stated in Standard Form
Graph a Line Given in Standard Form
Create a Line with a Given Slope
Determine the Slope of a Line Given Two Points on the Line
Graph a Line Given in Slope-Intercept Format
Determine the Slope and \(y\)-Intercept of a Line Whose Equation is Stated in Standard Form.
Determine the Equation of a Line Given Two Points on the Line
Solve a System of Equations Graphically.
Solve a System of Equations by Substitution.
Solve a System of Equations by Elimination.
Explore an Interest Systems Problem Numerically.
Explore an Acid Mixture Systems Problem Numerically.
Explore a Distance/Rate/Time Systems Problem Numerically.
Positive Integer Exponents
The Product Rule of Exponents
The Power-to-a-Power Rule of Exponents
The Power-to-a-Power and Product Rules of Exponents
The Quotient Rule of Exponents
The Quotient Rule of Exponents
The Quotient Rules of Exponents - Which One to Use
Practice Exponent Rules Applied to Non-Negative Integer Exponents
What's the Meaning of Negative Exponents?
Which Factors Move When There's a Negative Exponent?
Simplifying Expressions that Contain Integer Exponents
Scientific Notation
Scientific Notation
Scientific Notation Multiplication
FOIL
Simplify Square Root Expressions.
Rationalizing Monomial Denominators That Contain a Square Root Expression
Rationalizing Binomial Denominators That Contain Square Root Expressions
Explore the Meaning of Rational Exponents
Simplifying Square Roots of Negative Integers
Multiplication of Complex Numbers
Determine the Vertex of a Parabola Given in Standard Form - Part I
Determine the Vertex of a Parabola Given in Standard Form - Part II
Determine the Vertex of a Parabola Given in Standard Form - Part III
Using a Graph to Solve an Inequality - Part I
Using a Graph to Solve an Inequality - Part II
Determine the Greatest Common Factor
Determine the Greatest Common Factor
Show the Process of Factoring a Trinomial With a Leading Coefficient of One
Practice Factoring Trinomial With Leading Coefficients of One
Factoring by Grouping
Factoring Trinomials when the Leading Coefficient is not One - Part I
Factoring Trinomials when the Leading Coefficient is not One - Part II
Factoring Trinomials when the Leading Coefficient is not One - Part III
Factoring Difference of Squares that have One Variable
Factoring Difference of Squares that have Two Variables
Factoring Sum or Difference of Cubes that Have One Variable
Factoring Sum or Difference of Cubes that Have Two Variables
Introduction to Function Notation - Part One
Introduction to Function Notation - Part Two
Advanced Function Notation
Addition of Rational Expressions
Solving Rational Equations
Solving Quadratic Equations after Completing the Square
Graphing Parabolas when the Equation is in Vertex Form
Graphing Parabolas After Completing the Square when the Leading Coefficient is One
Graphing Parabolas After Completing the Square when the Leading Coefficient is Two
Graphing Parabolas After Completing the Square when the Leading Coefficient is Two
Graphical Transformations - Horizontal Shifts
Graphical Transformations - Vertical Shifts
Graphical Transformations - Horizontal and Vertical Shifts
Graphical Transformations - Axis Reflections
Graphical Transformations - Horizontal Stretches and Compressions
Graphical Transformations - Vertical Stretches and Compressions
Graphical Transformations - Stretches, Compressions, and Reflections
Graphical Transformations - \(g(x)=a \cdot f(b(x \pm h)) \pm k\)
Graphical Transformations - \(g(x)=a \cdot f(b x \pm h) \pm k\)
The Unit Circle and the Graph of the Sine Function
Unique Triangle - the Case of Side, Side, Side
Authored in PreTeXt
Section
17.71
Graphical Transformations - \(g(x)=a \cdot f(b x \pm h) \pm k\)
¶
Figure
17.71.1.
Practice Transformations based upon \(y=a \cdot f(bx-h)+k\text{:}\) Enter the coordinates for the shifted points A, B, C and then click "Show Transformed Curve" to check your answer.
login
