1. 7.1-7.2 Graphs of Exponential Functions

2. Exponential Function Where base (b), b > 0, b  1, and x is any real number.

3. Graphs of Exponential Equations To see the basic shape of an exponential function such as make a table of values and plot points.

4. xy -2 0 1 2 3 1 2 4 8 Graph f(x) = 2 x

5. Notice the end behavior of the graph. As x → + ∞, f(x) → +∞, which means that the graph moves up to the right. As x → - ∞, f(x) → 0, which means that the graph has the line y=0 as an asymptote. An asymptote is a line that a graph approaches (gets close to) as you move away from the origin.

8. Exponential Growth Function: The graph passes through the point (0,a) [the y-intercept]. Have these characteristics… Where a > 0 and b > 1 The x-axis is an asymptote of the graph. The domain is all real numbers. The range is y > 0 if a > 0

9. Identify the y-intercept and asymptote State the domain and range

10. What do you think would happen to the shift of the graph? h determines the horizontal shift k determines the vertical shift

11. Domain: All Real Numbers Range: All Positive Real Numbers Domain: All Real Numbers Range: y > -3 Asymptote: y = -3 Asymptote: y = 0

12. Domain: All Real Numbers Range: y > 2 Domain: All Real Numbers Range: y > 1 Asymptote: y = 2 Asymptote: y = 1

13. Exponential Decay Function Where a > 0, base b is 0 < b < 1 (b is a fraction), and x is any real number.

14. Decide whether f(x) is an exponential growth or exponential decay function. Because 0 < b < 1 f is an exponential decay function Because b > 1 f is an exponential growth function 1) 2)

15. Graphs of Exponential Equations To see the basic shape of an exponential function such as make a table of values and plot points.

16. xy -2 0 1 2 2 1 ½ ¼ Graph f(x) = (½) x -3

17. State the domain, range, make a table of values and graph the following

18. Homework: Page 482 #9-21 mult of 3; 25, 28-30 Page 489 #3-6, 12-24 mult of 3; 31