Precalculus: Key Concepts

Limit (informal)

The value a function approaches as the input approaches a given value

Continuous Function

A function with no breaks, holes, or jumps in its graph

Piecewise Function

A function defined by different expressions on different intervals

Even Function

f(-x) = f(x); symmetric about the y-axis

Odd Function

f(-x) = -f(x); symmetric about the origin

Horizontal Asymptote

y-value a function approaches as x → ±∞

Vertical Asymptote

x-value where a function approaches ±∞ (denominator = 0)

Parametric Equations

Expressing x and y as functions of a parameter t: x = f(t), y = g(t)

Polar Coordinates

(r, θ) — distance from origin and angle from positive x-axis

Polar to Rectangular

x = r cos θ, y = r sin θ