Exponential Functions Section 12.3 Exponential Functions
Exponential Function A function of the form f(x) = bx is called an exponential function if b > 0, b is not 1, and x is a real number.
Exponential Functions We can graph exponential functions of the form f(x) = 3x, g(x) = 5x 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: one-to-one function y-intercept (0, 1) no x-intercept domain is (−, ) range is (0, )
Example Graph the exponential functions f(x) = 2x and g(x) = 4x on the same set of axes. Continued
Example Graph the exponential functions and on the same set of axes. Continued
Graphs of Exponential Functions y We would find a pattern in the graphs of all the exponential functions of the type bx, where b > 1.
Graphs of Exponential Functions y We would find a pattern in the graphs of all the exponential functions of the type bx, where 0 < b < 1.
Example Graph the exponential function
Uniqueness of bx Let b > 0 and b 1. Then bx = by is equivalent to x = y.
Example Solve each equation for x. a. 6x = 36 b. 92x+1 = 81 c.
Example Solve 43x-6 = 322x