Graphing Functions

Pure Mathematics — Second Secondary

Graphs of the basic functions

Many complicated graphs are simply a basic graph that has been moved, stretched or flipped.
So we learn the shape of the basic graphs and their key points:

Function	Shape	Key point
f(x) = x²	A parabola opening upward	Vertex (0, 0)
f(x) = x³	An increasing curve through the origin	Origin (0, 0)
f(x) = \|x\|	A V-shape	Vertex (0, 0)
f(x) = √x	Half a parabola lying on its side to the right	Starting point (0, 0)
f(x) = 1/x	Two separate branches (a hyperbola)	Does not cross the y-axis

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