Precalculus Exponential and Logarithmic Functions Graphs of Functions
Graph of the Logarithmic Function Interactive Example 1

|  |  | Definition 1 |  |
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For a > 0 and a is not equal to 1, y = logax means ay = x.

|  |  | Definition 2 |  |
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If a > 0 and a is not equal to 1, then the logarithmic function of base a is defined to be f(x) = logax .

Graph of f(x) = log a x , 0 < a < 1 | Graph of f(x) = log a x , a > 1
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|  |  | Statement |  |
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PROPERTIES OF THE LOGARITHMIC FUNCTION The domain of f is the set of positive real numbers. The range of f is the set of all real numbers. The x-intercept for the graph of f is 1. The graph of f has no y-intercept. The y-axis is a vertical asymptote for the graph of f. The function f is increasing if a > 1 and decreasing if 0 < a < 1. The function f is one - to - one.

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