Gallery
Discover apps people built on Collabby by chatting. Run them, then remix to make them yours.
Chain Rule & Composite Functions
Run the inner and outer machines separately to see how their two slopes multiply to make the overall slope.
Related Rates
See how one rate of change drives another as a ladder slips and a balloon inflates.
Differential Equations & Slope Fields
Draw slopes on a grid, then add curves that follow them to see what solutions to differential equations look like.
Ordered Pairs and Coordinates
Ordered pairs pin down each spot—plot the points, find the target, and connect them in order to draw a house, a boat, and an arrow.
Parametric Plane Motion
Vary the parameter t and a projectile's initial speed and angle to trace the path of a point and see its velocity vector at each instant.
Matrices & Linear Transformations
Change the four entries of a matrix to transform grids and a house, and see how the determinant scales area and why the inverse vanishes when it is 0.
Taylor Polynomial Approximation
Raise the degree and shift the center of expansion to see how closely the Taylor polynomial hugs the curve and how fast the error shrinks.
Polar Coordinates & Curves
Adjust angle and radius to master polar coordinates, then graph roses, cardioids, and spirals from a single equation and compare them with Cartesian form.
Trigonometric Addition Formulas
Add two angles on the unit circle to verify the addition and double-angle formulas, then merge two waves into a single sine.
Derivatives, Maxima and Minima
Slide the tangent line to read the sign of the slope, locate maxima and minima where it changes, and find the largest fenced area for a fixed perimeter.
Translating and Reflecting Graphs
Shift with p and q, stretch with a and b, and move the minus sign around to see translations and reflections in the x-axis, y-axis, and origin.
Limits and Continuity
Approach a point from both sides to find limits, check the three conditions for continuity, and follow x without bound to reveal asymptotes.
Exponential and Logarithmic Functions
Exponential and logarithmic graphs mirror each other across y=x—see the reflection and handle a log scale that fits 1 and 1,000,000 on one screen.
Definite Integrals and Area
Slice ever-thinner rectangles under a curve to close in on the true area, and see why regions below the axis count as negative.
The Unit Circle and Trig Graphs
Rotate a point on the unit circle to see where sin and cos come from, then unfold it into a wave and reshape its amplitude and period.
Derivatives and Tangent Slopes
Slide two points together to watch the secant's slope approach the tangent's slope—the derivative at that point.
Speed, Distance and Time
Drive a car to work out speed = distance ÷ time, then send it back to see how distance travelled differs from displacement.
Is it a Function?
Slide a vertical line across graphs to see whether each x gives just one y, and decide which relations are functions.
Coordinate Plane Transformations
Translate, reflect, rotate, and scale a triangle to uncover the coordinate rules behind congruence and similarity.
Coordinate Plane & Proportions
Read coordinates and quadrants, then change the values to see direct proportion draw a line and inverse proportion a curve.
Solving Systems Graphically
Move two lines' slopes and intercepts to see the intersection as the solution of a system, and find what happens when lines are parallel or identical.
Quadratic Parabolas
Change a and the vertex (p, q) to see how a parabola flips, widens, and shifts, then match the target curve.
Graphs of Linear Functions
Adjust the slope a and the y-intercept b to see how a line tilts and where it crosses, then match target lines and predict the points it passes through.