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Unformatted text preview: c circlecopyrt Kendra Kilmer January 20, 2009 Section 2.4 - Exponential Functions Definition: The equation defines an exponential function for each real number b , called the base. Properties of the Graphs of f ( x ) = b x 1. Domain is the set of all real numbers. 2. Range is the set of all positive real numbers. 3. All graphs pass through the point ( , 1 ) . 4. The graph is continuous (no holes or jumps). 5. The x axis is a horizontal asymptote (but only in one direction). 6. If b > 1, the graph is increasing (exponential growth). 7. If 0 < b < 1, the graph is decreasing (exponential decay). Example 1: Graph f ( x ) = 2 x , g ( x ) = 5 x , h ( x ) = parenleftbigg 1 2 parenrightbigg x , and k ( x ) = parenleftbigg 1 5 parenrightbigg x . 13 c circlecopyrt Kendra Kilmer January 20, 2009 Definition: The most common base is the number e . Properties of Exponential Functions For a and b positive, a negationslash = 1, b negationslash = 1, and x and y real, 1. Exponent laws: a x a y = a x + y...
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