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20 results for "Functions".

Topic results

3 results

Functions

Use parent-curve moves, a shifted reciprocal family, and one exponential bench so graph moves, asymptotes, domain breaks, growth versus decay, and target-time questions stay tied to the same visual branch before the math path widens into local and accumulated change.

Math3 concepts
Open Functions

Calculus

Start from slope on the graph itself, use one constrained rectangle bench to make a real maximum visible, keep limit and continuity behavior available on one target point, and then widen into signed area and accumulation so rate and total change stay connected on one visual branch.

Math4 concepts
Open Calculus

Vectors

Use one 2D plane to read vectors as arrows, ordered pairs, matrix actions, alignment measures, and projections before the same language bridges into motion.

Math3 concepts
Open Vectors

Starter track results

2 results

Functions and Change

Keep the first math path compact: read parent-curve moves first, then rational asymptotes and domain breaks, then exponential growth and decay, local slope, visible limit behavior, and finally accumulation so change stays graph-first all the way through.

Math6 concepts
Open Functions and Change

Complex and Parametric Motion

Start with complex numbers as points on one plane, turn that plane into unit-circle and polar-coordinate geometry, deepen that same bench into trig identities and inverse-angle reasoning, then carry the coordinate language into motion traced from x(t) and y(t).

Math6 concepts
Open Complex and Parametric Motion

Guided collection results

1 result

Functions and Change Lesson Set

Use the functions topic page, the existing graph-first starter track, one accumulation checkpoint, and the calculus topic page so the early math branch stays compact for a teacher-led lesson block.

MathLesson set
Open lesson set

Goal path results

1 result

Build function and rate intuition from the graph first

Use the functions topic page, the new lesson set, the compact math starter track, and the calculus topic page so graph moves, rational asymptotes, exponential change, local slope, and accumulation stay on one coherent bench.

MathBuild intuition
Open goal path

Concept results

12 results

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

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

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

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

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

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

Subject results

1 result

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.

Math4 topics
Open Math