1. Coordinated Algebra Unit 3 Part B

2. What is an Exponential Function?

3. Examples…

4. Applications…  Population Growth  Science (Bacterial Growth, Radiation, Half-Life, etc.)  Investments/Finance  Appreciation and Depreciation

5. Let’s examine exponential functions. They are different than any of the other types of functions we’ve studied because the independent variable is in the exponent. Let’s look at the graph of this function by plotting some points. x 2 x 3 8 2 4 1 2 0 1 -1 1/2 -2 1/4 -3 1/8 2-7-6-5-4-3-21573 0468 7 1 2 3 4 5 6 8 -2 -3 -4 -5 -6 -7 Recall what a negative exponent means: BASE

6. Compare the graphs 2 x, 3 x, and 4 x Characteristics about the Graph of an Exponential Function where a > 1 What is the domain of an exponential function? 1. Domain is all real numbers What is the range of an exponential function? 2. Range is positive real numbers What is the x intercept of these exponential functions? 3. There are no x intercepts because there is no x value that you can put in the function to make it = 0 What is the y intercept of these exponential functions? 4. The y intercept is always (0,1) because a 0 = 1 5. The graph is always increasing Are these exponential functions increasing or decreasing? 6. The x-axis (where y = 0) is a horizontal asymptote for x  -  Can you see the horizontal asymptote for these functions?