Common Functions Reference

Here are some of the most commonly used functions, and their graphs:

Linear Function:

Graph of a straight line y = mx + b

f(x) = mx + b

Square Function:

Graph of y = x squared, a parabola opening upwards through the origin

f(x) = x2

Cube Function:

Graph of y = x cubed, passing through the origin from bottom-left to top-right

f(x) = x3

Square Root Function:

Graph of y = square root of x, starting at (0,0) and curving into the first quadrant

f(x) = √x

Reciprocal Function

Graph of y = 1/x, showing two hyperbolic curves in the first and third quadrants

f(x) = 1/x

Logarithmic Function:

Graph of y = ln(x), passing through (1, 0) and increasing slowly
f(x) = ln(x)

Floor and Ceiling Functions:

Step graph of the floor function with solid dots on the left of each step
The Floor Function
Step graph of the ceiling function with solid dots on the right of each step
The Ceiling Function

Sign Function

Dance Moves

You can remember them by dancing (author unknown):

Cartoon character using arm positions to mimic function shapes like parabolas and lines

7250, 7251, 7252, 7253, 7254, 7255, 7256, 7257, 7258, 7259