What Even Power Functions Do Near Zero and at Infinity

Local Behavior of Odd Power Functions Near Zero

End Behavior of Exponential Functions

This Always Happens with Parabolas

This Is What Completing the Square Is Really Doing

Determining End Behavior of a Polynomial Function

Average Rate of Change on a Closed Interval

The 2 main components of math as a whole

A visual example of how rate of change works

The Definition of Average Rate of Change

Domain Restrictions from Square Roots in the Denominator

Recommending a non-math course to my students?!

This Is Where Domain Problems Get Interesting

Understanding imaginary numbers

The Cleanest Way to See Subsets of the Real Numbers

Interval Notation Explained To My Precal Students

Conceptual Foundations of Domain and Range

Algebraic Reduction of the Difference Quotient

Setting Up the Difference Quotient for a Quadratic

Understanding Stereographic Projection on the Circle

Showing Two Metrics Generate the Same Topology

The Picture That Makes This Proof Make Sense

A Practical Definition of Open Sets in Metric Topology

How Bounded Metrics Change Geometry

How Bijections Can Induce New Metrics

How Metrics Generate Topologies

P2 – Turning the Picture into a Proof (Hausdorff Spaces)

P1 - The One Picture That Explains Hausdorff Spaces

If You Understand This, You Understand Topology

Continuity via Preimages: A Topological Proof

Understanding Discontinuity Without Limits

The Topological Definition of Continuity Explained

From Bases to Topologies: A Visual Proof

Why Unions of Basis Elements Form a Topology

Understanding Bases in Topology

Why a Single Missing Point Can Ruin Everything…

How to Negate the Definition of Associativity

Constructing the Rational Numbers Using Equivalence Classes

Why 1/2 and 2/4 Are the Same Number: The Real Reason

Understanding Formal Fractions Before Defining Rational Numbers

The Smallest and Largest Equivalence Relation Explained

Meet the Map Where Doing It Twice Gives You Back X

One Trick to Know If a Function Is Invertible

The Truth Table That Blows Students’ Minds

Did you know this logic trick?

This Is Why Local Maxima Have Zero Slope

Stop Memorizing Set Operations — SEE Them Instead

Every Group of Order pq, Listed