Function Library
Each page below covers one notable function in depth: what it is, its key mathematical properties, where it shows up — plus a panel of properties computed live by the calculator's own math engine (roots, extrema, intercepts, derivatives, and integrals).
Sine Function
f(x) = sin(x)
The classic wave of trigonometry: a smooth oscillation that repeats every 2π.
Cosine Function
f(x) = cos(x)
The even, wave-shaped sibling of sine — cosine starts at its peak and repeats every 2π.
Tangent Function
f(x) = tan(x)
A repeating curve that climbs from −∞ to +∞, with vertical asymptotes wherever cosine hits zero.
Quadratic Function
f(x) = x^2 - 4
The parabola x² − 4: a U-shaped curve with roots at ±2 and its lowest point at (0, −4).
Cubic Function
f(x) = x^3 - 3*x
An S-shaped cubic with three real roots, a local hill and valley, and 180° rotational symmetry.
Exponential Function
f(x) = e^x
The function that is its own derivative — constant relative growth, forever increasing, never touching zero.
Natural Logarithm Function
f(x) = log(x)
The inverse of eˣ — it unwraps exponential growth, turning multiplication into addition.
Square Root Function
f(x) = sqrt(x)
The gentle half-parabola — the inverse of squaring, defined for x ≥ 0.
Absolute Value Function
f(x) = abs(x)
The V-shaped measure of distance from zero — simple, symmetric, with a corner at the origin.
Reciprocal Function
f(x) = 1/x
The hyperbola 1/x — two mirror branches divided by asymptotes on both axes.