Fundamental Functions & Graphs

Absolute Value Function

The graph of y = |x| forms a V-shape, where all outputs are non-negative.

$Graph of Absolute Value Function$

The graph of y = x is a straight line passing through the origin with a slope of 1.

$Graph of Linear Function$

The graph of y = x ² is a parabola opening upwards, with its vertex at the origin.

$Graph of Quadratic Function$

The graph of y = x ³ shows an S-shaped curve passing through the origin.

$Graph of Cubic Function$

The graphs of y = a ^x and y = -a ^x represent exponential growth and decay.

$Graph of Exponential Functions$

The graphs of y = a ^x and y = a ^-x show growth and decay with an inverse relationship.

$Graph of Inverse Exponential Functions$

The graph of y = e ^x illustrates continuous exponential growth with base e .

$Graph of Natural Exponential Function$

The graph of y = √x is a curve in the first quadrant, showing non-negative outputs.

$Graph of Square Root Function$

The graph of y = ∛x passes through the origin and shows symmetry about the origin.

$Graph of Cubic Root Function$

The graph of y = ln(x) shows a curve that grows slowly and is undefined for x≤0 .

$Graph of Natural Logarithmic Function$

The graph of y = sin(x) oscillates between -1 and 1, with a period of 2π .

$Graph of Sine Function$

The graph of y = cos(x) oscillates between -1 and 1, similar to the sine function but shifted.

$Graph of Cosine Function$

The graph of y = tan(x) has periodic vertical asymptotes and repeats every π .

$Graph of Tangent Function$

The graph of y = cot(x) is periodic with vertical asymptotes and repeats every π .

$Graph of Cotangent Function$