Graphing and Analyzing Rational Functions

Precalculus & Trigonometry

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Functions - Properties and Their Graphs — Topic Review

Study Guide (fill this in as you watch the videos!)
Quick Overview of Functions (p. 3-5) (13:48)
The Difference Quotient (p. 6) (6:23)
Finding The Domain of a Function (p. 7) (6:03)
Adding Subtracting Multiplying and Dividing Functions (p. 8-9) (13:10)
Graphs (p. 10-12) (9:54)
Graphing with a Calculator (p. 13) (6:21)
Even vs Odd vs Neither (p. 14-15) (8:23)
Increasing Decreasing Constant (p. 16) (3:38)
Local Maxima and Local Minima (p. 17-18) (9:48)
Average Rate of Change and Secant Lines (p. 19) (2:54)
Thinking of Old Things in New Ways (p. 20-21) (9:17)
Direct Inverse and Combined/Joint Variation (p. 22-24) (10:31)

Functions - Properties & Their Graphs — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Quick Overview of Functions Practice Exam Solutions (5:16)
The Difference Quotient Practice Exam Solutions (24:38)
Finding the Domain of a Function Practice Exam Solutions (14:09)
Adding, Subtracting, Multiplying, and Dividing Functions Practice Exam Solutions (16:12)
Graphs Practice Exam Solutions (8:27)
Even vs Odd vs Neither Practice Exam Solutions (5:35)
Average Rate of Change and Secant Lines Practice Exam Solutions (9:10)

Graphing and Transforming Functions — Topic Review (⏱️ <41 min)

Study Guide (fill this in as you watch the videos!)
Important Types of Parent Functions (p. 3-4) (11:47)
Piecewise Functions (p. 5) (7:50)
Transforming a Function (p. 6-9) (20:51)

Graphing and Transforming Functions — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Piecewise Functions Practice Exam Solutions (12:40)
Transforming Functions Practice Exam Solutions (34:13)

Linear Functions — Topic Review (⏱️ <12 min)

Study Guide (fill this in as you watch the videos!)
Quick Overview of Linear Functions (p. 3-4) (6:12)
Word Problems and Modeling with Linear Functions (p. 5) (5:21)

Linear Functions — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Overview of Linear Functions Practice Exam Solutions (6:31)
Word Problems with Linear Functions Practice Exam Solutions (10:27)

Quadratic Functions — Topic Review (⏱️ <47 min)

Study Guide (fill this in as you watch the videos!)
Quick Overview of Quadratic Functions (p. 3-5) (11:52)
Properties of Quadratics (p. 6-7) (5:43)
Graphing a Quadratic Using Its Vertex, Axis of Symmetry, and Intercepts (p. 8) (9:36)
Graphing a Quadratic Using Transformations (p. 9-10) (6:57)
Maximum/Minimum Value of a Quadratic (p. 11) (6:06)
Complex Numbers and Quadratics (p. 12-13) (6:52)

Quadratic Functions — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Overview of Quadratic Functions Practice Exam Solutions (10:36)
Graphing Quadratics Practice Exam Solutions (23:15)
Finding Maxima and Minima of Quadratic Functions Practice Exam Solutions (10:16)
Complex Numbers and Quadratics Practice Exam Solutions (15:25)

Absolute Value Functions — Topic Review (⏱️ <12 min)

Study Guide (fill this in as you watch the videos!)
Equations with Absolute Value (p. 3) (3:22)
Inequalities with Absolute Value (p. 4-5) (8:27)

Absolute Value Functions — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Equations with Absolute Value Practice Exam Solutions (7:15)
Inequalities with Absolute Value Practice Exam Solutions (9:21)

Polynomial Functions — Topic Review (⏱️ <96 min)

Study Guide (fill this in as you watch the videos!)
Quick Overview of Polynomial Functions (p. 3-4) (5:08)
Graphing Using Transformations (p. 5-6) (10:11)
Real Zeros and Multiplicities (p. 7-8) (7:17)
Turning Points (p. 9) (4:44)
End Behavior (p. 10) (5:19)
Graphing Using Zeros and Multiplicities (p. 11-12) (19:01)
Finding Real Zeros of Polynomials (p. 13-14) (7:40)
Descartes’ Rule of Signs and Rational Zeros Theorem (p. 15-17) (12:32)
Putting It All Together to Find Zeros (p. 18) (9:32)
Fundamental Theorem of Algebra (p. 19-21) (14:17)

Polynomial Functions — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Graphing Using Transformations Practice Exam Solutions (11:18)
Graphing Using Zeros and Multiplicities Practice Exam Solutions (23:12)
Forming Polynomial Functions Practice Exam Solutions (4:53)
Remainder Theorem - Practice Exam Questions Video Solutions (3:35)
Descartes' Rule of Signs Practice Exam Solutions (9:48)
Rational Zeros Theorem Practice Exam Solutions (14:18)
Fundamental Theorem of Algebra Practice Exam Solutions (6:46)

Rational Functions — Topic Review (⏱️ <75 min)

Study Guide (fill this in as you watch the videos!)
Quick Overview of Rational Functions and Domain (p. 3) (4:38)
Vertical Asymptotes of Rational Functions (p. 4) (3:09)
Horizontal and Oblique Asymptotes of Rational Functions (p. 5-8) (19:50)
Holes of Rational Functions (p. 9) (2:27)
Graphing Rational Functions (p. 10-12) (23:17)
Applications with Rational Functions (p. 13) (5:24)
Inequalities with Rational Functions and Polynomials (p. 14-15) (14:49)

Rational Functions — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Graphing and Analyzing Rational Functions - Practice Exam Solutions (8:31)
Inequalities with Rational Functions Practice Exam Solutions (14:44)

Exponential Functions — Topic Review (⏱️ <23 min)

Study Guide (fill this in as you watch the videos!)
Exponential Functions (p. 3-5) (14:31)
The Number e (p. 6) (2:06)
Solving Exponential Equations (p. 7-8) (6:36)

Exponential Functions — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Graphing Exponential Functions Practice Exam Solutions (31:14)
Solving Exponential Equations Practice Exam Solutions (7:16)

Log Functions — Topic Review (⏱️ <75 min)

Study Guide (fill this in as you watch the videos!)
Log Functions (p. 3-4) (13:07)
Graphing Log Functions (p. 5-7) (13:44)
Log Rules (p. 8-11) (15:49)
Solving Equations with Logs (p. 12-14) (16:22)
Solving Equations with Exponentials (p. 15-16) (11:52)
Summary of Log and Exponent Rules (p. 17) (3:53)

Log Functions — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Graphing Log Functions Practice Exam Solutions (21:51)
Log Rules Practice Exam Solutions (10:58)
Solving Equations with Logs Practice Exam Solutions (22:49)

Applications of Logs and Exponents — Topic Review (⏱️ <57 min)

Study Guide (fill this in as you watch the videos!)
Finance Applications - Overview (p. 3-5) (15:31)
Effective Rate of Interest (p. 6) (6:20)
Present Value (p. 7) (5:40)
Exponential Growth and Decay (p. 8-10) (21:10)
Newton's Law of Cooling (p. 11) (7:17)

Applications of Logs and Exponents — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Finance Applications Practice Exam Solutions (6:54)
Exponential Growth and Decay Practice Exam Solutions (7:10)
Newton's Law of Cooling Practice Exam Solutions (7:40)

Trig Functions — Topic Review (⏱️ <84 min)

Study Guide (fill this in as you watch the videos!)
All About Angles (p. 3-6) (20:03)
Arc Length (p. 7) (1:58)
Area of a Sector (p. 8) (2:54)
Linear Speed and Angular Speed (p. 9) (5:57)
Right Triangle Trig (p. 10-13) (22:02)
Some Special Right Triangles (p. 14-16) (12:43)
Summary of All Important Angles (p. 17) (10:12)
Applications to Measuring Heights and Distances (p. 18) (7:14)

Trig Functions — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
All About Angles - Practice Exam Solutions (13:00)
Right Triangle Trig - Practice Exam Solutions (15:20)

The Unit Circle — Topic Review (⏱️ <37 min)

Trig Functions of Any Angle - The Unit Circle (p. 3-5) (13:47)
Trig Functions of Any Angle - Locating Angles (p. 6-7) (10:56)
The Quick Way of Evaluating ANY Trig Function (p. 8-10) (12:33)

The Unit Circle — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
The Unit Circle Practice Exam Solutions (30:32)
Finding Other Trig Functions Practice Exam Solutions (10:41)

Graphing Trig Functions — Topic Review (⏱️ <72 min)

Study Guide (fill this in as you watch the videos!)
Quick Review of Transforming a Function (p. 3-5) (9:35)
Graphs of Sine and Cosine (p. 6-7) (9:28)
Procedure for Graphing Sine and Cosine (p. 8-10) (23:29)
Graphs of Tangent and Cotangent (p. 11-12) (10:51)
Graphs of Secant and Cosecant (p. 13-15) (13:56)
Summary of Sh*t to Memorize (p. 16-17) (4:33)

Graphing Trig Functions — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Graphs of Trig Functions Practice Exam Solutions (49:06)

Inverse Trig — Topic Review (⏱️ <94 min)

Study Guide (fill this in as you watch the videos!)
Inverse Sine - Overview (p. 3-5) (9:39)
Inverse Cosine - Overview (p. 6-8) (8:22)
How to Evaluate Compositions with Inverse Sine (p. 9-10) (8:47)
How to Evaluate Compositions with Inverse Cosine (p. 11-12) (7:21)
Inverse Tangent - Overview (p. 13-14) (8:18)
How to Evaluate Compositions with Inverse Tangent (p. 15-16) (9:50)
Finding Inverses with Equations Involving Trig Functions (p. 17-18) (5:54)
Evaluating Mixed Trig Function Expressions (p. 19-23) (12:55)
Inverse Secant, Cosecant, and Cotangent (p. 24-25) (6:53)
The Super Fast Way to Evaluate Inverse Trig Expressions (p. 26-28) (12:22)
Summary of Shit to Memorize (p. 29) (3:48)

Inverse Trig — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Evaluating Basic Inverse Sine, Cosine, and Tangent Expressions Practice Exam Solutions (8:17)
Evaluating Composite Inverse Sine, Cosine, and Tangent Expressions Practice Exam Solutions (11:10)
Solving Equations with Inverse Trig Practice Exam Solutions (4:06)
Evaluating Inverse Secant, Cosecant, and Cotangent Expressions Practice Exam Solutions (4:16)
Evaluating Mixed Trig Expressions Practice Exam Solutions (12:51)

Trig Identities — Topic Review (⏱️ <72 min)

Study Guide (fill this in as you watch the videos!)
Quick Overview of Trig Identities (p. 3-6) (12:07)
Double Angle Formulas (p. 7-8) (13:34)
Half-Angle Formulas (p. 9-10) (15:39)
Sum and Difference Formulas (p. 11-13) (16:23)
Product-to-Sum Formulas (p. 14) (4:45)
Sum-to-Product Formulas (p. 15-16) (6:34)
Summary of Sh*t to Memorize (p. 17) (3:05)

Trig Identities — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Double-Angle Formulas Practice Exam Solutions (4:10)
Half-Angle Formulas Practice Exam Solutions (10:56)
Sum and Difference Formulas Practice Exam Solutions (16:33)
Product-to-Sum Formulas Practice Exam Solutions (6:59)
Sum-to-Product Formulas Practice Exam Solutions (5:08)
Establishing Identities Practice Exam Solutions (21:57)

Trig Equations — Topic Review (⏱️ <30 min)

Study Guide (fill this in as you watch the videos!)
Solving Basic Trig Equations (p. 3-5) (17:20)
Solving Trig Equations - Quadratic Forms (p. 6-8) (11:57)

Trig Equations — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Solving Trig Equations Practice Exam Solutions (29:36)

Trig Applications — Topic Review (⏱️ <58 min)

Study Guide (fill this in as you watch the videos!)
Applications with Right Triangles (p. 3-5) (13:22)
Law of Sines Overview and Unambiguous Case (p. 6-7) (9:42)
Law of Sines Ambiguous Case (SSA Triangles) (p. 8-10) (19:03)
Law of Cosines (p. 11-12) (15:38)

Trig Applications — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Applications with Right Triangles Practice Exam Solutions (6:46)
Law of Sines Practice Exam Solutions (9:18)
Law of Cosines Practice Exam Solutions (13:23)

Sequences and Series — Topic Review

Study Guide (fill this in as you watch the videos!)
Sequences (p. 3-5) (13:24)
Summations (Series) (p. 6-7) (10:39)
Arithmetic Sequences (p. 8-9) (9:26)
Geometric Sequences (p. 10-11) (14:22)

Sequences and Series — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Sequences Practice Exam Solutions (3:11)
Summations Practice Exam Solutions (4:38)
Arithmetic Sequences Practice Exam Solutions (6:20)
Geometric Sequences Practice Exam Solutions (5:33)

Preview of Calculus — Topic Review (⏱️ <43 min)

Study Guide (fill this in as you watch the videos!)
Limits from Tables and Graphs (p. 3-4) (6:34)
Limits Algebraically (p. 5-8) (6:18)
Continuity (p. 9-10) (8:55)
Tangent Lines and the Derivative (p. 11-12) (8:39)
Area and the Integral (p. 13-15) (8:51)
Using a Graphing Calculator to Evaluate an Integral (p. 16) (3:44)

Preview of Calculus — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Limits Practice Exam Solutions (3:45)
Continuity Practice Exam Solutions (4:46)
Tangent Lines and the Derivative Practice Exam Solutions (2:05)
Area and the Integral Practice Exam Solutions (4:07)

Polar Coordinates — Topic Review (⏱️ <80 min)

Study Guide (fill this in as you watch the videos!)
Polar Coordinates Overview (p. 3-4) (8:09)
Converting Points from Polar to Rectangular Coordinates (p. 5-6) (8:37)
Converting Points from Rectangular to Polar Coordinates (p. 7) (8:05)
Transforming Equations from Polar to Rectangular Form (p. 8) (3:56)
Transforming Equations from Rectangular Form to Polar Form (p. 9) (3:26)
Polar Equations and Graphs Overview (p. 10-13) (9:53)
Graphing Circles in Polar Form (p. 14-15) (6:38)
Graphing Cardioids and Limaçons (p. 16-19) (16:27)
Graphing Roses (p. 20-22) (14:47)

Polar Coordinates — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Converting Between Rectangular and Polar Coordinates Practice Exam Solutions (19:28)
Polar Equations and Graphs Practice Exam Solutions

Vectors — Topic Review (⏱️ <38 min)

Study Guide (fill this in as you watch the videos!)
Vectors - Overview (p. 3) (5:54)
Geometric Vectors (p. 4-5) (7:33)
Algebraic Vectors (p. 6-8) (12:09)
Unit Vectors (p. 9) (3:35)
Components of Vectors (p. 10-11) (8:40)

Vectors — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
Finding Vectors From Points Practice Exam Solutions (2:04)
Operations on Algebraic Vectors Practice Exam Solutions (7:44)
Components of Vectors Practice Exam Solutions (12:00)

Conics — Topic Review (⏱️ <48 min)

Study Guide (fill this in as you watch the videos!)
Quick Overview of Conics (p. 3) (2:10)
The Parabola (p. 4-5) (14:47)
The Ellipse (p. 6-7) (16:18)
The Hyperbola (p. 8-9) (14:28)

Conics — Practice Exam Questions

Practice Exam Questions
Practice Exam Questions Answer Key
The Parabola Practice Exam Solutions (13:33)
The Ellipse Practice Exam Solutions (41:50)
The Hyperbola Practice Exam Solutions (27:15)

[OPTIONAL] Sh*t You Forgot from Algebra 1

Study Guide (fill this in as you watch the videos!)
Algebraic Expressions (p. 3) (5:43)
Exponent Rules (p. 4-5) (8:08)
Square Roots (p. 6) (2:45)
Monomials and Polynomials (p. 7-8) (5:57)
Special Products and Factoring (p. 9-12) (19:55)
Lines (Quick Overview) (p. 13) (4:04)
Finding Equations and Graphing Lines (p. 14-17) (13:45)
General Form of a Line (p. 18) (3:06)
Vertical and Horizontal Lines (p. 19) (2:19)
Parallel and Perpendicular Lines (p. 20) (5:09)
Plotting Points to Graph an Equation (p. 21-22) (5:40)
Finding Intercepts from a Graph (p. 23) (1:33)
Finding Intercepts from an Equation (p. 24) (4:13)
Solving Equations with Absolute Value (p. 25) (5:33)
Number Lines and Inequalities (p. 26) (5:05)
Solving Inequalities and Writing Intervals (p. 27-29) (12:44)
Solving Inequalities with Absolute Value (p. 30-31) (14:22)
Completing the Square (p. 32-35) (9:58)
Solving Quadratics by Factoring (p. 36) (5:35)
Solving Quadratics by Using Square Roots (p. 37) (2:39)
Solving Quadratics by Completing the Square (p. 38) (8:43)
Solving Quadratics by Using the Quadratic Formula (p. 39) (5:38)
Sets (p. 40-41) (8:47)

[OPTIONAL] Sh*t You Forgot from Geometry

Study Guide (fill this in as you watch the videos!)
The Pythagorean Theorem (p. 3) (5:10)
Common Geometry Formulas (p. 4-5) (3:19)
Congruent Triangles (p. 6-7) (4:08)
Similar Triangles (p. 8-10) (8:34)
Distance Formula (p. 11) (7:59)
Midpoint Formula (p. 12) (5:26)
Graphing Circles (p. 13-14) (7:32)
General Form of a Circle (p. 15-16) (11:09)

[OPTIONAL] Sh*t You Forgot from Algebra 2

Study Guide (fill this in as you watch the videos!)
Parent Graphs You Should Memorize (p. 3) (2:09)
Graphing Common Equations (p. 4) (2:36)
Symmetry of Graphs (p. 5) (8:22)
Solving Equations by Factoring (p. 6-7) (11:20)
Long Division with Numbers and Polynomials (p. 8-10) (14:18)
Synthetic Division (p. 11-13) (7:39)
Multiplying and Dividing Fractions (p. 14-16) (10:16)
Adding and Subtracting Fractions (p. 17-18) (16:24)
Simplifying Complex Fractions (p. 19-20) (6:29)
Solving Systems of Linear Equations (p. 21-22) (10:04)
General Tips for Solving Word Problems (p. 23) (5:25)
Simple Interest Word Problems (p. 24) (3:47)
Some Perfect Roots You Should Memorize (p. 25) (5:00)
Radical Rules (p. 26) (4:28)
Combining Like Terms with Radicals (p. 27) (3:26)
Rationalizing a Denominator (p. 28) (5:43)
Fractional (Rational) Exponents (p. 29-31) (18:53)
Operations with Complex Numbers (p. 32-34) (11:41)
Patterns in the Powers of i (p. 35) (4:31)
Solving Quadratic Equations that Have Complex Solutions (p. 36) (8:19)

Graphing and Analyzing Rational Functions - Practice Exam Solutions

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