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Example 7
Draw the graph of [ x ] where [ x ] denotes the greatest integer not greater than x.
Solution : The Graph of [ x ] consists of the portions of
lines defined in the domains as under:
y = 0 for 0 £ x < 1
y = 1 for 1 £ x < 2
y = 2 for 2 £ x < 3
y = -1 for -1 £ x < 0
y = -2 for -2 £ x < -1
and so on.
The right hand end point of the each segment id not the point of the graph.
(III) Analytical Representation of a function
: If the functional relation y = f(x) is such that 'd'
denotes an analytical expression, we say that the function y of
x is represented analytically. For example:
(i) y = x2 - 7
(ii) 
(iii) 
(iv) y = cos x
(v) y = px 2
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