2. Graphing Exponential Functions

3. What you need to know… To find the y-intercept of an exponential function, evaluate f(0). The y-intercept has the coordinates (0, f(0)). To locate the y-intercept of a graphed function, determine the coordinates of the function where the line crosses the y-axis. To find the x-intercept in function notation, set f(x) = 0 and solve for x. The x-intercept has the coordinates (x, 0).

4. What else? To locate the x-intercept of a graphed function, determine the coordinates of the line where the line crosses the x-axis. Not all exponential functions cross the x-axis. The asymptote of exponential functions of the form f(x) = ab x is always the x-axis, or y = 0. If the exponential function is of the form f(x) = ab x + k, then the function will be shifted vertically by the same number of units as k.

5. And… The asymptote is then y = k. The end behavior, or the behavior of the graph as x becomes larger or smaller, will always be one of three descriptions: infinity, negative infinity, or the asymptote. It is easiest to first graph the function and then observe what happens to the value of y as the value of x increases and decreases. Graph complex exponential models using technology as values can become quite large or small very quickly.

6. Practice 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.

7. Create a table of values. Choose values of x and solve for the corresponding values of f(x).

8. Identify the asymptote of the function In the function f(x) = –1(3)x – 2, the value of k is –2. The asymptote of the function is y = –2 The asymptote of the function is always the constant, k

9. 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, –3).

10. Graph the function. Use the table of values to create a graph of the function

11. Describe the end behavior of the graph. The end behavior is what happens at the ends of the graph. As x becomes larger, the value of the function approaches negative infinity. As x becomes smaller, the value of the function approaches the asymptote, – 2.

12. THANKS FOR WATCHING! ~DR. DAMBREVILLE