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Theorem 1

THEOREM 1

The exponential function y = ax is increasing if a > 1, constant if a = 1, and decreasing if a < 1.

08_exp-log_functions-6.gif

Figure 8.1.2

PROOF

Inequality (vi) shows that ax is increasing if a > 1.

If a < 1 and q < r then 1/a > 1, (1/a)q < (1/a)r, aq > ar so ax is decreasing.

If a = 1 then ax = 1 is constant.

Figure 8.1.2 shows graphs of y = ax for different values of a.

 
Home Exponential and Logartihmic Functions Exponential Functions Theorem 1

Last Update: 2006-11-05