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