Chapter 2.5

Graphs of Basic Functions

Continuity

Earlier in this chapter we graphed linear functions. The graph of a linear function, a straight line, may be drawn by hand over any interval of its domain without picking the pencil up from the paper.

In mathematics we say that a function with this property is continuous ouver any interval. The formal definition of continuity requires concepts from calculus, but we can give an informal definition at the college algebra level.

If a function is not continuous at a point, then it has a discontinuity at the point where x = 2.

Example 1 Determining Intervals of Continuity

Describe the intervals of continuity for each function if Figure 52

Example 1 Determining Intervals of Continuity

Describe the intervals of continuity for each function if Figure 52

Graphs of the basic functions studied in college algebra can be sketched by careful point plotting or generated by a graphing calculator. As you become more familiar with these graphs you should be able to provide quick rough sketches of them.

y

x

Example 2 Graphing Piecewise-Defined Functions

2 xif 1x

2 xif 52xxf

Graph each function

y

x

Example 2 Graphing Piecewise-Defined Functions

1 xif 6x-

1 xif 32xxf

Graph each function

y

x

xxf Graph