Lesson 3.6 (Continued) Graphing Exponential Functions : Graphing Exponential Functions

2 Initial value Horizontal Asymptote

: Graphing Exponential Functions

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 : Graphing Exponential Functions

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

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 = ____ : Graphing Exponential Functions

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, ____) : Graphing Exponential Functions

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

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

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 : Graphing Exponential Functions

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

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 = ____ : Graphing Exponential Functions

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, ____) : Graphing Exponential Functions

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

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

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 : Graphing Exponential Functions

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

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 = ____ : Graphing Exponential Functions

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, ___) : Graphing Exponential Functions

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

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

Your turn……

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

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