Course Content
Composite and Inverse Functions
0/5
Composite Functions
Modeling with Composite Functions
Invertible Functions
Inverse Functions in Graphs and Tables
Verifying Inverse Functions by Composition
Trigonometry
0/10
Special Trigonometric Values in the First Quadrant
Trigonometric Identities on the Unit Circle
Inverse Trigonometric Functions
Law of Sines
Law of Cosines
Solving General Triangles
Sinusoidal Equations
Sinusoidal Models
Angle Addition Identities
Using Trigonometric Identities
Complex Numbers
0/9
The Complex Plane
Distance and Midpoint of Complex Numbers
Complex Conjugates and Dividing Complex Numbers
Identities with Complex Numbers
Modulus and Argument of Complex Numbers
Polar Form of Complex Numbers
Graphically Multiplying Complex Numbers
Multiplying and Dividing in Polar Form
The Fundamental Theorem of Algebra
Rational Functions
0/7
Reducing Rational Expressions to Lowest Terms
End Behavior of Rational Functions
Discontinuities of Rational Functions
Graphs of Rational Functions
Modeling with Rational Functions
Multiplying and Dividing Rational Expressions
Adding and Subtracting Rational Expressions
Conic Sections
0/6
Intro to Conic Sections
Center and Radii of an Ellipse
Foci of an Ellipse
Intro to Hyperbolas
Foci of a Hyperbola
Hyperbolas Not Centered at the Origin
Vectors
0/9
Vector Introduction
Vector Components
Magnitude of Vectors
Scalar Multiplication
Vector Addition and Subtraction
Direction of Vectors
Vector Components from Magnitude and Direction
Adding Vectors in Magnitude and Direction Form
Vector Word Problems
Matrices
0/15
Intro to Matrices
Using Matrices to Represent Data
Multiplying Matrices by Scalars
Adding and Subtracting Matrices
Properties of Matrix Addition & Scalar Multiplication
Using Matrices to Manipulate Data
Matrices as Transformations of the Plane
Using Matrices to Transform the Plane
Transforming 3d and 4D Vectors with Matrices
Multiplying Matrices by Matrices
Properties of Matrix Multiplication
Representing Systems of Equations with Matrices
Intro to Matrix Inverses
Finding Inverses of 2×2 Matrices
Solving Linear Systems with Matrices
Probability and Combinatorics
0/9
Venn Diagrams and the Addition Rule
Multiplication Rule for Probabilities
Permutations
Combinations
Probability Using Combinatorics
Probability Distributions Intro
Theoretical & Empirical Probability Distributions
Decisions with Probability
Expected Value
Series
0/3
Geometric Series
Geometric Series (with Summation Notation)
The Binomial Theorem
Limits and Continuity
0/15
Defining Limits and Using Limit Notation
Estimating Limit Values from Graphs
Estimating Limit Values from Tables
Determining Limits Using Algebraic Properties of Limits: Limit Properties
Determining Limits Using Algebraic Properties of Limits: Direct Substitution
Determining Limits Using Algebraic Manipulation
Selecting Procedures for Determining Limits
Determining Limits Using the Squeeze Theorem
Exploring Types of Discontinuities
Defining Continuity at a Point
Confirming Continuity Over an Interval
Removing Discontinuities
Connecting Infinite Limits and Vertical Asymptotes
Connecting Limits at Infinity and Horizontal Asymptotes
Working with the Intermediate Value Theorem
Precalculus

Explanation

Graphs of rational functions often include:

  • Vertical asymptotes

  • Horizontal or slant asymptotes

  • Holes

  • Intercepts

Steps to graph:

  1. Find restrictions

  2. Identify vertical asymptotes

  3. Find horizontal/slant asymptotes

  4. Find x- and y-intercepts

  5. Sketch behavior near asymptotes

Quiz

  1. What feature appears when a denominator equals zero?

  2. What type of asymptote shows end behavior?

  3. Can rational graphs have holes?

  4. What intercept occurs when y = 0?

  5. Do graphs ever touch vertical asymptotes?

Answer Key

  1. Vertical asymptote or hole

  2. Horizontal or slant asymptote

  3. Yes

  4. x-intercept

  5. No

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