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Precalculus 12: The Complete Video Guide
Transforming Functions
Translating Functions Vertically and Horizontally (12:14)
Reflecting Functions Over the X-Axis and Y-Axis (3:20)
Sketching the Graph of a Reflected Function (5:52)
Stretching and Compressing Functions (7:53)
Sketching the Graph of a Stretched Function (4:00)
Combining Translations, Reflections, and Stretches (16:27)
Inverse Relations and Functions (12:24)
Radical Functions
Properties of Radical Functions (5:03)
Transforming a Radical Function (4:46)
Sketching the Graph of the Square Root of a Function (6:02)
Solving a Radical Equation (1:59)
Polynomial Functions
Dividing Polynomials by Binomials Using Long Division (15:13)
Using Synthetic Division (4:46)
Factoring Polynomials (14:20)
Properties of Polynomial Functions (16:05)
Sketching the Graph of a Polynomial Function (9:05)
Word Problems (10:53)
Rational Functions
Properties of Rational Functions (2:35)
Vertical Asymptotes and Points of Discontinuity (7:15)
Horizontal Asymptotes and Oblique Asymptotes (7:30)
Sketching the Graph of a Rational Function (7:18)
Solving a Rational Equation (3:10)
Exponential Functions
Properties of Exponential Functions (10:28)
Transforming an Exponential Function (10:54)
Solving an Exponential Equation (13:22)
Logarithms
Logarithm Basics (11:46)
Logarithm Laws (20:45)
Logarithmic Functions
Properties of Logarithmic Functions (9:32)
Transforming a Logarithmic Function (9:10)
Solving a Logarithmic (and Exponential) Equation (14:44)
Trigonometry
Review from Math 11 (32:53)
Arc Length and Radians (29:37)
Trigonometric Ratios (15:46)
Trigonometric Functions
Properties of Trigonometric Functions (11:59)
Sketching the Graph of a Trigonometric Function (17:05)
Trigonometric Equations and Identities
Solving Trigonometric Equations (28:12)
Trigonometric Identites (21:03)
Proving Trigonometric Identities (24:52)
Solving Trigonometric Equations Using Identities (12:53)
Function Operations
Properties of Combined Functions (5:20)
Combining Functions Graphically (6:01)
Composite Functions
Properties of Composite Functions (4:05)
Finding the Equation of a Composite Function (10:19)
Finding the Value of a Composite Function (3:31)
Finding the Composition of a Function (8:52)
Counting Principles
The Fundamental Counting Principle (22:36)
Factorial Notation (3:54)
Permutations (26:34)
Combinations (28:13)
The Binomial Theorem (19:07)
Finding a Specific Term of an Expansion (6:53)
Sketching the Graph of a Stretched Function
Example #1
use the equation to recognize the transformations y = af(bx)
choose multiple points to transform, (x, y) becomes ((1/b)x, ay)
plot new points and connect them
Example #2
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