1. Lesson 3.6 (Continued) Graphing Exponential Functions 1 3.4.2: Graphing Exponential Functions

2. 2 Initial value Horizontal Asymptote

3. 3 3.4.2: Graphing Exponential Functions

4. Guided Practice Example 1 Create a table of values for the exponential function f(x) = –1(3) x – 2. Identify the asymptote and y-intercept of the function. Plot the points and sketch the graph of the function, and describe the end behavior. 4 3.4.2: Graphing Exponential Functions

5. Guided Practice: Example 1, continued 1.Create a table of values. Choose values of x and solve for the corresponding values of f(x). 5 3.4.2: Graphing Exponential Functions xf(x)f(x) -2 0 1 2

6. Guided Practice: Example 1, continued 2.Identify the asymptote of the function. The asymptote of the function is always the constant, k. In the function f(x) = –1(3) x – 2, the value of k is –2. The asymptote of the function is y = ____. 6 3.4.2: Graphing Exponential Functions

7. Guided Practice: Example 1, continued 3.Determine the y-intercept of the function. The y-intercept of the function is the value of f(x) when x is equal to 0. It can be seen in the table that when x = 0, f(x) = –3. The y-intercept is (0, ____). 7 3.4.2: Graphing Exponential Functions

8. Guided Practice: Example 1, continued 4.Graph the function. Use the table of values to create a graph of the function. 8 3.4.2: Graphing Exponential Functions

9. Guided Practice: Example 1, continued 5.Describe the end behavior of the graph. As x +∞, y ____ As x -∞, y ____ 9 3.4.2: Graphing Exponential Functions ✔

10. Guided Practice Example 2 Create a table of values for the exponential function. Identify the asymptote and y-intercept of the function. Plot the points and sketch the graph of the function, and describe the end behavior. 10 3.4.2: Graphing Exponential Functions

11. Guided Practice: Example 2, continued 1.Create a table of values. Choose values of x and solve for the corresponding values of f(x). 11 3.4.2: Graphing Exponential Functions xf(x)f(x) –2 –1 0 1 2

12. Guided Practice: Example 2, continued 2.Identify the asymptote of the function. The asymptote of the function is always the constant, k. In the function, the value of k is –3. The asymptote of the function is y = ____. 12 3.4.2: Graphing Exponential Functions

13. Guided Practice: Example 2, continued 3.Determine the y-intercept of the function. The y-intercept of the function is the value of f(x) when x is equal to 0. It can be seen in the table that when x = 0, f(x) = -7. The y-intercept is (0, ____). 13 3.4.2: Graphing Exponential Functions

14. Guided Practice: Example 2, continued 4.Graph the function. Use the table of values to create a graph of the function. 14 3.4.2: Graphing Exponential Functions

15. Guided Practice: Example 2, continued 5.Describe the end behavior of the graph. As x +∞, y ____ As x -∞, y ____ 15 3.4.2: Graphing Exponential Functions ✔

16. Guided Practice Example 3 Create a table of values for the exponential function f(x) = –1(2) x – 3. Identify the asymptote and y-intercept of the function. Plot the points and sketch the graph of the function, and describe the end behavior. 16 3.4.2: Graphing Exponential Functions

17. Guided Practice: Example 3, continued 1.Create a table of values. Choose values of x and solve for the corresponding values of f(x). 17 3.4.2: Graphing Exponential Functions xf(x)f(x) -2 0 1 2

18. Guided Practice: Example 3 continued 2.Identify the asymptote of the function. The asymptote of the function is always the constant, k. In the function f(x) = –1(2) x – 3, the value of k is –3. The asymptote of the function is y = ____. 18 3.4.2: Graphing Exponential Functions

19. Guided Practice: Example 3, continued 3.Determine the y-intercept of the function. The y-intercept of the function is the value of f(x) when x is equal to 0. It can be seen in the table that when x = 0, f(x) = –4. The y-intercept is (0, ___). 19 3.4.2: Graphing Exponential Functions

20. Guided Practice: Example 3, continued 4.Graph the function. Use the table of values to create a graph of the function. 20 3.4.2: Graphing Exponential Functions

21. Guided Practice: Example 3, continued 5.Describe the end behavior of the graph. As x +∞, y ____ As x -∞, y ____ 21 3.4.2: Graphing Exponential Functions ✔

22. Your turn……

23. Asymptote: y-intercept: Domain: Range: End behavior:

24. Asymptote: y-intercept: Domain: Range: End behavior: