## Example 6.2.1:

Which of the two functions is intuitively continuous and which
one is not ?

Since Descartes claims that a function is continuous if its graph
can be drawn without lifting the pencil, we will look at the graph
of each function:
*f(x) = 1*if*x > 0*and*f(x) = -1*if*x < 0*. Is this function continuous ?*f(x) = 5x - 6*. Is this function continuous?

*f(x) = -1*if

*x < 0*and

*1*if

*x > 0*: Since we have to lift the pencil to draw this graph, this function does not appear to be continuous.

*f(x) = 5x - 6*: Since this graph, being a straight line, does not require us to lift the pencil, we would call this function continuous.