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Precalculus - Functions, Inverse Trigonometry, Polar Coordinates, and Complex Numbers

Krista King via YouTube

Overview

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Master essential precalculus concepts through this comprehensive video playlist covering inverse trigonometric functions, polar coordinates, graphing polar curves, parametric equations, analytic geometry, and complex numbers. Explore fundamental function properties including domain, range, and the vertical line test, then advance to function classification, even and odd functions, and piecewise functions. Learn equation modeling techniques for real-world applications and master various forms of linear equations including point-slope and slope-intercept forms. Develop skills in graphing parabolas and circles, finding centers and radii, and working with function combinations and compositions. Study function transformations both algebraically and graphically, determine one-to-one functions, and find inverse functions. Practice advanced algebraic techniques including logarithmic simplification using laws of logarithms, solving quadratic equations with the quadratic formula and completing the square, and performing polynomial long division for rational functions. Conclude with trigonometric concepts including hyperbolic identities and memorization strategies for the unit circle, providing a solid foundation for calculus studies.

Syllabus

Calculus - Functions (KristaKingMath)
Which functions pass the VERTICAL LINE TEST?!! (KristaKingMath)
How to find DOMAIN AND RANGE for a function (KristaKingMath)
Finding values and domain and range from a graph (KristaKingMath)
Determining if a function is even, odd or neither (KristaKingMath)
How to classify functions (KristaKingMath)
Equation Modeling (KristaKingMath)
Modeling the equation of a piecewise defined function from its graph (KristaKingMath)
Sketching a graph from a story problem (KristaKingMath)
Equation of a line in point-slope form (KristaKingMath)
Equation of the line in slope-intercept form (KristaKingMath)
Least squares line (KristaKingMath)
Sketch the graph of a parabola (KristaKingMath)
How to find the CENTER AND RADIUS of a circle (KristaKingMath)
Sketch the graph of a circle (KristaKingMath)
Combinations of functions and their domains (KristaKingMath)
Composite functions (KristaKingMath)
Composite functions and their domains (KristaKingMath)
Describing transformations algebraically (KristaKingMath)
Using transformations to sketch a graph (KristaKingMath)
Determine whether a function is 1 to 1 (KristaKingMath)
How to find the INVERSE OF A FUNCTION (KristaKingMath)
Finding the linear function given two points on its inverse (KristaKingMath)
Use laws of logarithms to simplify a logarithmic function (KristaKingMath)
Use the quadratic formula to find roots of the function (KristaKingMath)
Completing the square of a quadratic function (KristaKingMath)
Polynomial long division for rational functions (KristaKingMath)
Hyperbolic identities (KristaKingMath)
How to remember the unit circle (KristaKingMath)

Taught by

Krista King

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