1. 8.1 Exponential Functions ©2001 by R. Villar All Rights Reserved

2. Exponential Functions Exponential Function: An equation in the form f(x) = Ca x. Recall that if 0 < a < 1, the graph represents exponential decay and thatif a > 1, the graph represents exponential growth Examples: f(x) = (1/2) x f(x) = 2 x Exponential DecayExponential Growth We will take a look at how these graphs “shift” according to changes in their equation...

3. Take a look at how the following graphs compare to the original graph of f(x) = (1/2) x : f(x) = (1/2) x f(x) = (1/2) x + 1 f(x) = (1/2) x – 3 Vertical Shift: The graphs of f(x) = Ca x + k are shifted vertically by k units.

4. Take a look at how the following graphs compare to the original graph of f(x) = (2) x : f(x) = (2) x f(x) = (2) x – 3 f(x) = (2) x + 2 – 3 Horizontal Shift: The graphs of f(x) = Ca x – h are shifted horizontally by h units. Notice that f(0) = 1 (0,1) Notice that this graph is shifted 3 units to the right. (3,1) Notice that this graph is shifted 2 units to the left and 3 units down. (-2,-2)

5. Take a look at how the following graphs compare to the original graph of f(x) = (2) x : f(x) = (2) x f(x) = –(2) x f(x) = –(2) x + 2 – 3 Notice that f(0) = 1 (0,1) This graph is a reflection of f(x) = (2) x. The graph is reflected over the x-axis. (0,-1) Shift the graph of f(x) = (2) x,2 units to the left. Reflect the graph over the x-axis. Then, shift the graph 3 units down (-2,-4)