Use x for y = f(x), or a full equation such as x^2+y^2=4. Operators: + − * / ^; functions: sin, cos, tan, abs, sqrt, cbrt, exp, ln, log10; constants pi, e. Angles are radians.

Easy: ten graph types, each using one parent function with simple scales or shifts. Medium: sixteen types with more transformations, sums and products. Hard: 3D surfaces.

Try x^3 for a cubic, cbrt(x) for a cube root (including negative x), sqrt(x) for a square root, 2^x for growth, or 0.5^x / exp(-x) for decay. Use ln(x) for the natural logarithm. Roots and logarithms must be defined throughout the displayed interval. Multiplication between numbers needs *, e.g. 3 * 2^x.

Explore the ideas: parent functions & transformations and exponential growth & decay (OpenStax).

Three equations. Five guesses each. Match all three exactly to unlock one shape bonus round; its points add to your total. Your highest-scoring guess counts. Error is RMS difference across the shown domain, divided by the target’s vertical range. For implicit curves and surfaces, error is symmetric RMS nearest-boundary distance within the shown box, divided by the box diagonal. Red shading shows the region between boundaries; in 3D, red bands connect the surfaces. Round points = (8,000 × fit + algebraic component points) × guess factor × time factor. Fit = e^(−6 × error). Algebraic components share a 2,000-point budget: function types, scales, shifts, reflections, and combined terms earn separate credit. Recognizing a transformation earns its component credit; fit judges the numerical values. Unmatched extra components reduce the credit per match. Equivalent exact fits earn all 2,000 points. The component breakdown shows points before guess, time, and hint deductions. Each extra guess costs 8%; time gradually reduces points by up to 35%. A numerically exact match across the plotted area finishes the round. Equivalent expressions count. Showing a hint halves that round’s points.

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