Continuity (Informal Definition)
A function is continuous over an interval of its
domain if its hand-drawn graph over that interval
can be sketched without lifting the pencil from the
paper. Discontinuity
If a function is not continuous at a point, then it may have a point of discontinuity, or it may have a vertical asymptote. Increasing
The range values increase from left to right
The graph rises from left to right
Decreasing
The range values decrease from left to right
The graph falls from left to right
To decide whether a function is increasing, decreasing, or constant on an interval, ask yourself “What does the graph do as x goes from left to right?” If we were to “fold” the graph of f (x) = x2 along the y-axis,
the two halves would coincide exactly. We refer to this
property as symmetry.