Comprehensive Graphing Techniques for Algebra, Precalculus, and Calculus

Explore comprehensive graphing techniques across multiple mathematics levels through this extensive video compilation covering intermediate algebra through calculus. Master inequalities in two variables, piecewise-defined functions, and fundamental graphing transformations before advancing to quadratic, rational, exponential, and logarithmic function graphs. Develop proficiency in trigonometric function graphing including sine, cosine, tangent, cotangent, cosecant, and secant functions, along with phase shift concepts and polar coordinate graphing. Study conic sections in detail including parabolas, ellipses, and hyperbolas, then progress to parametric equations and plane curves. Apply advanced curve sketching techniques from calculus including comprehensive analysis methods for rational functions, identifying holes and oblique asymptotes, and sketching exponential, trigonometric, and logarithmic functions. Conclude with three-dimensional graphing concepts covering cylinders and quadric surfaces from multivariable calculus, providing a complete foundation for graphing across all undergraduate mathematics levels.

Syllabus

Intermediate Algebra: Inequalities in Two Variables (Video #16) | Math with Professor V
Precalculus: Library of Functions; Piecewise-Defined Functions (Video #8) | Math with Professor V
Precalculus: Graphing Techniques-Tranformations (Video #9) | Math with Professor V
Precalculus: Quadratic Functions and Their Properties (Video #12) | Math with Professor V
Precalculus: The Graph of a Rational Function (Video #16) | Math with Professor V
Precalculus: Exponential Functions (Video #22) | Math with Professor V
Precalculus: Logarithmic Functions (Video #23) | Math with Professor V
Precalculus: Graphs of the Sine and Cosine Functions (Section 6.4) | Math with Professor V
Precalculus: Graphs of Tangent, Cotangent, Cosecant & Secant Functions (Section 6.5) | Professor V
Precalculus: Phase Shift (Section 6.6) | Math with Professor V
Polar Equations & Graphs (Trigonometry/Precalculus) | Math with Professor V
Precalculus: Conic Sections/The Parabola (Sections 10.1 & 10.2) | Math with Professor V
Precalculus: The Ellipse (Section 10.3) | Math with Professor V
Precalculus: The Hyperbola (Section 10.4) | Math with Professor V
Precalculus: Plane Curves and Parametric Equations (Section 10.7) | Math with Professor V
Calculus 1: Summary of Curve Sketching (Section 4.5) | Math with Professor V
Calculus 1: Curve Sketching Rational Functions, Graphs with Holes & Oblique Asymptotes | Professor V
Calculus 1: Curve Sketching Continued--Exponential, Trig, & Log Functions | Math with Professor V
Calculus 3: Cylinders and Quadric Surfaces (Video #6) | Math with Professor V