Home page for accesible maths Math 101 Chapter 2: Functions of a real variable 2.7 Parabolas 2.9 Discontinuous real functions

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2.8 Continuous and discontinuous graphs

A real function is continuous if we can draw the complete graph without removing pen from paper. Otherwise, the function is said to be discontinuous.

2.8.1 Example

The sine function is continuous. Here $f:{\mathbb{R}}\rightarrow{\mathbb{R}}:$ $f(x)=\sin x$ .

2.8.2 Example

Let $\lfloor x\rfloor$ be the largest integer $n$ such that $n\leq x$ . Then $g:{\mathbb{R}}\rightarrow{\mathbb{R}}:$ $g(x)=\lfloor x\rfloor$ gives the integer part function.