Graphing Techniques

Eddie Woo via YouTube

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Learn comprehensive graphing techniques through this extensive video series covering fundamental mathematical functions and their visual representations. Master linear relationships including step graphs and piecewise functions, explore parabolic transformations and modifications, and understand exponential and logarithmic function behavior. Develop skills in sketching curves using calculus, plotting polynomial functions, and analyzing rational functions with asymptotes. Practice graphing absolute value functions, hyperbolas, and circles while learning to solve inequalities visually. Study function transformations including translations, reflections, dilations, and compressions across various function types. Apply graphing methods to solve intersection problems, analyze function restrictions, and tackle exam-style questions involving tangent lines and geometric applications.

Syllabus

Addition & Subtraction of Ordinates (1 of 3)
Addition & Subtraction of Ordinates (2 of 3)
Addition & Subtraction of Ordinates (3 of 3)
Curve Sketching w/ Calculus (Basic Example)
Graphing Transformations (Reciprocal Function, Vertical Stretch & Horizontal Shift)
Linear Relationships (1 of 3): Review
Linear Relationships (2 of 3): Step Graphs
Linear Relationships (3 of 3): Piecewise Functions
What are Graphs? (Introduction & Metaphor)
Linear Graph Review: Comparing Different Gradients
Linear Graph Review: Sketching
Linear Graph Review: x & y Intercepts
Linear Graph Review: Vertical & Horizontal Lines
Introduction to Parabolas (1 of 3: Testing Values)
Introduction to Parabolas (2 of 3: Plotting Points)
Introduction to Parabolas (3 of 3: Drawing & Shifting)
Modifications of x² (1 of 2: Review of Shifts)
A little extra bit: what about y = x³ and x = y²?
Modifications of x² (2 of 2: Parabolas through the Origin)
Drawing Parabolas with a Template (1 of 2: Introduction)
Drawing Parabolas with a Template (2 of 2: Example Question)
Exponential Graphs (1 of 2: Considering the Values)
Review: Linear & Parabolic Graphs
Exponential Graphs (2 of 2: Plotting Points)
Introduction to the Hyperbola (1 of 2: Mathematical Modelling)
Introduction to the Hyperbola (2 of 2: Basic Shape & Characteristics)
Solving Linear Inequalities
Solving Linear Inequalities
Solving Quadratic Inequalities
Problem Solving w/ Linear Functions
Functions Requiring Restrictions
Graphing Logarithmic Functions (1 of 4: Basic + Shift)
Graphing Logarithmic Functions (2 of 4: Shift + Compression)
Graphing Logarithmic Functions (3 of 4: Tricky Powers)
Graphing Logarithmic Functions (4 of 4: Reflections)
Parabolas: Summary of Cartesian Formulas
Parabolas: Axis of Symmetry & Vertex
Graphing Parabolas (1 of 2: Step-by-Step Guide)
Graphing Parabolas (2 of 2: Simple Example)
Finding Points of Intersection Using Quadratics
Reviewing Factors of Functions (1 of 3: Factorising f(x), f(x+2) & f(x-2))
Reviewing Factors of Functions (2 of 3: Why Factorise? | Implications for Geometrical Shape)
Reviewing Factors of Functions (3 of 3: Table of Values to verify translation of x^2)
Translations of the Parabola (1 of 2: Finding the equation from its features)
Translations of the Parabola (2 of 2: Updated standard forms)
Finding the intersection point of two graphs
Graphing Polynomials (1 of 4: Fundamental graphs)
Solving Inequalities with Graphs (4 of 4: A secondary algebraic technique)
Solving Inequalities with Graphs (3 of 4: Hyperbola example)
Solving Inequalities with Graphs (2 of 4: Polynomial example)
Solving Inequalities with Graphs (1 of 4: Understanding the visual approach)
Graphing Rational Functions (4 of 4: Harder example - constructing graph)
Graphing Rational Functions (3 of 4: Harder example - identifying features)
Graphing Rational Functions (2 of 4: Basic example)
Graphing Rational Functions (1 of 4: Understanding asymptotes)
Graphing Exponentials & Logs (5 of 5: Reflected logarithmic graph)
Graphing Exponentials & Logs (4 of 5: Translated logarithmic graph)
Graphing Exponentials & Logs (3 of 5: Reflected exponential graphs)
Graphing Exponentials & Logs (2 of 5: Overview of transformations)
Graphing Exponentials & Logs (1 of 5: Fundamental graphs)
Graphing Absolute Value Functions (3 of 3: Reflections & non-linear curves)
Graphing Absolute Value Functions (2 of 3: Translations)
Graphing Absolute Value Functions (1 of 3: Definitions)
Graphing Polynomials (4 of 4: Dilation)
Graphing Polynomials (3 of 4: Vertical translation)
Graphing Polynomials (2 of 4: Horizontal translation)
Graphing Techniques Q&A (3 of 3: Solving an inequality visually)
Graphing Techniques Q&A (2 of 3: Vertical transformation example)
Graphing Techniques Q&A (1 of 3: Horizontal transformation example)
Graphing a Logarithmic Function - example test question
Equation of Circle from Tangent [Exam Question]