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Functions and ChangeFunctionsGraph transforms

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Functions3 conceptsCalculus4 conceptsVectors3 conceptsComplex Numbers and Parametric Motion6 concepts

Functions

3 concepts
Open FunctionsOpen Math

Graph Transformations

Move one parent curve with honest controls so shifts, vertical scale, and reflections stay tied to the same overlaid graph and landmark points.

MathFunctions
Open Graph transforms

Rational Functions / Asymptotes and Behavior

Vary one shifted reciprocal family so domain breaks, vertical and horizontal asymptotes, intercepts, and removable-hole behavior stay tied to the same graph.

MathFunctions
Open Rational functions

Exponential Change / Growth, Decay, and Logarithms

Change one starting value, one rate, and one target so growth, decay, doubling or half-life, and logarithmic target time all stay tied to the same live curve.

MathFunctions
Open Exponential change

Calculus

4 concepts
Open CalculusOpen Math

Derivative as Slope / Local Rate of Change

Slide a point along one curve, tighten a secant into a tangent, and connect local steepness to the derivative graph without leaving the same live bench.

MathCalculus
Open Derivative as slope

Limits and Continuity / Approaching a Value

Move one target-distance slider inward from both sides, compare the finite-limit guide with the actual point, and separate continuous, removable-hole, jump, and blow-up behavior on one graph-first bench.

MathCalculus
Open Limits and continuity

Optimization / Maxima, Minima, and Constraints

Move one rectangle width under a fixed 24 meter perimeter and watch height, area, and local slope respond together so the square maximum emerges from the same bench.

MathCalculus
Open Optimization and constraints

Integral as Accumulation / Area

Drag one upper bound across a source curve, watch signed area and the accumulation graph update together, and separate current source height from the running total.

MathCalculus
Open Integral as area

Vectors

3 concepts
Open VectorsOpen Math

Vectors in 2D

Combine, subtract, and scale vectors on one plane so magnitude, direction, and components stay tied to the same live object.

MathVectors
Open 2D vectors

Matrix Transformations / Stretch, Shear, Reflection

Let one 2 by 2 matrix act on a grid, the basis vectors, and a sample shape so stretch, shear, reflection, and combined plane changes stay visual instead of symbolic-only.

MathVectors
Open Matrix transforms

Dot Product / Angle and Projection

Keep two vectors, their angle, the signed projection of one onto the other, and the dot product visible together so alignment reads geometrically instead of as memorized cases.

MathVectors
Open Dot product

Complex Numbers and Parametric Motion

6 concepts
Open Complex Numbers and Parametric MotionOpen Math

Complex Numbers on the Plane

Read complex numbers as points and vectors on one plane, then keep addition and multiplication geometric instead of symbolic-only.

MathComplex Numbers and Parametric Motion
Open Complex numbers

Unit Circle / Sine and Cosine from Rotation

Keep one rotating point, its x and y projections, and the sine-cosine traces linked so the unit circle becomes the live source of both functions.

MathComplex Numbers and Parametric Motion
Open Unit circle rotation

Polar Coordinates / Radius and Angle

Keep one point visible in polar and Cartesian views at the same time so radius and angle turn directly into x and y on the plane.

MathComplex Numbers and Parametric Motion
Open Polar coordinates

Parametric Curves / Motion from Equations

Keep x(t), y(t), the traced path, and the moving point visible together so shape and traversal stay distinct.

MathComplex Numbers and Parametric Motion
Open Parametric curves

Trig Identities from Unit-Circle Geometry

Keep one rotating point and its projections visible so the core trig identities stay tied to geometry instead of detached symbol rules.

MathComplex Numbers and Parametric Motion
Open Trig identities

Inverse Trig / Angle from Ratio

Keep one polar point and its coordinate signs visible so inverse trig becomes angle-from-ratio reasoning with quadrant checks instead of a calculator-only output.

MathComplex Numbers and Parametric Motion
Open Inverse trig

Focused branch

Show Math topic pages and paths

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Newer subject branch4 topics2 starter tracks

Math

Enter the current math slice through graph transformations, rational-function asymptotes, exponential change, vectors, complex-plane geometry, trig identities, inverse-angle reasoning, polar coordinates, and parametric motion without leaving the same live-bench product language used elsewhere on the site.

Fastest honest route

Functions and Change is still the clearest bounded start, while the collection and goal-path links keep the newer subject layer one click away.

Topic

Functions

Starter track

Functions and Change

Lesson set

Functions and Change Lesson Set

Goal path

Build function and rate intuition from the graph first
Open MathStart Functions and Change