This document discusses exponential functions and their graphs. It covers the basic exponential function f(x) = a^x where a is a positive number. Examples are given of evaluating basic exponential functions at different values of x. The one-to-one property of exponential functions is demonstrated. The graph of the basic exponential function f(x) = 2^x is shown and its asymptote is identified as the line y = 0. Shifting and reflecting the graph are discussed, and it is noted how the asymptote changes with shifting.

1. 5.1 Exponential Functions and Their Graphs A. Basic Exponential Function (increasing and decreasing) B. One-to-one property C. Graph of Basic Exponential Function including Asymptote D. Shifting Graph of Basic Exponential Function (including asymptote)

3. Suppose f(x) = 2 x . Find f(4).

5. Suppose f(x) = (1/3) x . Find f(4).

9. You try:

11. Let’s compare that shape to f(x)=4 x x f(x)=4 x (x,y) 0 1 4 0 =1 4 1 = (0,1) ( -1 -2 4 -1 = 4 -2 = -3 2 4 -3 = 4 2 =

16. You try: Shift f(x) = 2 x to the left 2 units. Gve the equation, the graph, and the asymptote.

17. You try: Reflect f(x) = 2 x over the x-axis. Give the equation, the graph, and the asymptote.