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**Unformatted text preview: **§ 12.3 Exponential Functions Martin-Gay, Beginning and Intermediate Algebra, 4ed 2 Exponential Expressions We have previously worked with exponential expressions, where the exponent was a rational number The expression b x can actually be defined for all real numbers, x , including irrational numbers. However, the proof of this would have to wait until a higher level math course. Martin-Gay, Beginning and Intermediate Algebra, 4ed 3 Exponential Functions A function of the form f ( x ) = b x is called an exponential function if b > 0, b is not 1, and x is a real number. Exponential Functions Martin-Gay, Beginning and Intermediate Algebra, 4ed 4 We can graph exponential functions of the form f ( x ) = 3 x , g ( x ) = 5 x or h ( x ) = (½) x by substituting in values for x , and finding the corresponding function values to get ordered pairs. We would find all graphs satisfy the following properties: • 1-to-1 function • y-intercept (0, 1) • no x-intercept • domain is (- ∞ , ∞ ) • range is (0, ∞ ) Exponential Functions Martin-Gay, Beginning and Intermediate Algebra, 4ed 5 We would find a pattern in the graphs of all the exponential functions of the type b x , where b > 1....

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