Exponential Functions Pre-Algebra 12-6 Exponential Functions Warm Up Write the rule for each linear function. 1. 2. f(x) = -5x - 2 f(x) = 2x + 6

Learn to identify and graph exponential functions.

An exponential function has the form f(x) = p  ax, where a > 0 and a ≠ 1. If the input values are the set of whole numbers, the output values form a geometric sequence. The y-intercept is f(0) = p. The expression ax is defined for all values of x, so the domain of f(x) = p  ax is all real numbers.

Example A: Graphing an Exponential Function Create a table for the exponential function, and use it to graph the function. A. f(x) = 3  2x x y –2 –1 1 2 3 4 3  2-2 = 3  1 4 3  2-1 = 3  1 2 3 2 3 3  20 = 3  1 6 3  21 = 3  2 12 3  22 = 3  4

Example B: Graphing an Exponential Function Create a table for the exponential function, and use it to graph the function. B. f(x) = 4  1 2 x x y –2 –1 1 2 4  = 4  4 1 2 –2 16 4  = 4  2 1 2 –1 8 4  = 4  1 1 2 4 4  = 4  1 2 1 2 4  = 4  1 2 2 1 4 1

Example C Create a table for the exponential function, and use it to graph the function. C. f(x) = 2x x y –2 –1 1 2 1 4 2-2 1 2 2-1 1 20 2 21 4 22

Example D Create a table for the exponential function, and use it to graph the function. D. f(x) = 2x+ 1 x y –2 –1 1 2 5 4 2-2 + 1 3 2 2-1 + 1 2 20 + 1 3 21 + 1 5 22 + 1

If a > 1, the output f(x) gets larger as the input x gets larger If a > 1, the output f(x) gets larger as the input x gets larger. In this case, f is called an exponential growth function.

Lesson Review: Part 1 1. Create a table for the exponential function f(x) = , and use it to graph the function. 3  1 2 x x y –2 12 –1 6 3 1 2 3 4 3 2