Graphs of common functions

The graphs you meet in IB, A Level and IGCSE maths, each with its domain, range, intercepts, turning points and asymptotes, how to sketch it and how it is transformed. Open any of them in the free Grapher to explore.

Graph of y = x² (y = x^2) drawn on a grid and its key points marked — The graph of y = x², drawn by the Grapher.

Straight lines

y = x
y = 2x + 1
y = 3 − 2x

Quadratics

y = x²
y = −x²
y = x² − 4
y = (x − 2)²
y = x² − 2x − 3
y = 2x² − 4x + 1

Cubics

y = x³
y = −x³
y = x³ − x
y = x³ − 3x
y = x³ − 3x² + 4

Quartics

y = x⁴
y = x⁴ − 2x²

Square roots and cube roots

y = √x
y = √(4 − x²)
y = ∛x

Reciprocal and rational functions

y = 1/x
y = −1/x
y = 1/x²
y = 1/(x − 2) + 3
y = (2x + 1)/(x − 1)
y = x + 1/x
y = 1/(x² + 1)

Modulus (absolute value)

y = |x|
y = |x − 2|
y = |x² − 4|

Exponential functions

y = eˣ
y = e⁻ˣ
y = 2ˣ
y = (1/2)ˣ
y = e^(−x²)
y = xeˣ

Logistic curve

y = 1/(1 + e⁻ˣ)

Logarithms

y = ln x
y = log₁₀ x
y = log₂ x
y = ln(x + 2)
y = ln|x|
y = x ln x

Trigonometric functions

y = sin x
y = cos x
y = tan x
y = sin 2x
y = 2 sin x + 1
y = sec x
y = cosec x
y = cot x

Inverse trigonometric functions

y = arcsin x
y = arccos x
y = arctan x

Explore with the Grapher

Graph transformations with sliders
Table of values calculator
Intersections and turning points
Open the Grapher

The Grapher is our own free tool (graph.mathrevision.co.uk), built for IB, A Level and IGCSE students. It is not an exam calculator: practise on your own GDC for calculator papers.