Скачать или смотреть AP Precalculus UNIT 1 Review: Polynomial and Rational Functions (Reteaching Test Practice Problems)

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Unit 1: Polynomial and Rational Functions

1.1 Change in Tandem
1.2 Rates of Change
1.3 Rates of Change in Linear and Quadratic Functions
1.4 Polynomial Functions and Rates of Change
1.5 Polynomial Functions and Complex Zeros
1.6 Polynomial Functions and End Behavior
1.7 Rational Functions and End Behavior
1.8 Rational Functions and Zeros
1.9 Rational Functions and Vertical Asymptotes
1.10 Rational Functions and Holes
1.11 Equivalent Representations of Polynomial and Rational Expressions
1.12 Transformations of Functions
1.13 Function Model Selection and Assumption Articulation
1.14 Function Model Construction and Application

In this video, I thoroughly describe and reteach the main components of the sections listed above found in the official College Board AP Precalculus course description found at https://apcentral.collegeboard.org/me.... Afterwords, I provide multiple examples and give descriptive solutions to AP Precalculus-style problems. Topics in this video include…

*1. Key Concepts in Calculus:*
Concave Up: Graph curves upward (2nd derivative positive).
Concave Down: Graph curves downward (2nd derivative negative).
Inflection Points: Where concavity changes.
Rate of Change: How fast y changes with x.
Average Rate of Change: Overall change over an interval.
Linearity or Quadratic Nature: Identifying linear or quadratic behavior.

*2. Polynomial Functions and Properties:*
Graphs of Polynomials: Degree, leading coefficient, behavior.
Local Extrema: Local maxima and minima.
Absolute Extrema: Highest and lowest points.
Factoring Polynomials: Breaking them into simpler parts.
Multiplicity: How many times a root appears.
Complex Numbers: Real + imaginary parts.
Even and Odd Functions: Symmetry properties.
Limit Notation: Behavior near specific values.

*3. Rational Functions and Regression Analysis:*
Zeros (Roots): Points where the function equals zero.
Vertical Asymptotes: Lines where function approaches infinity.
End Behavior: How function behaves at +/- infinity.
Holes (Point Discontinuities): Removable discontinuities.
Multiplicity: Number of times a root appears.
Slant Asymptotes: Diagonal asymptotes.
Limit Notation: Behavior as x approaches a value.

*4. Binomial Theorem, Function Transformations, and Regression Analysis:*
Binomial Theorem: Expanding (a + b)^n.
Function Transformations: Shifting, stretching, reflecting.
Linear Models: Representing linear relationships.
Quadratic Models: Describing parabolic shapes.
Cubic Models: Analyzing cubic relationships.
Using TI-83 Plus for Regression: Linear, quadratic, and cubic regression with a TI-83 Plus calculator.

These concepts are fundamental in precalculus and serve as building blocks for more advanced mathematical topics.

I have many informative videos for Pre-Algebra, Algebra 1, Algebra 2, Geometry, Pre-Calculus, and Calculus. Please check it out:    / nickperich  

Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa
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