Final answer:
To graph the function f(x) = 2(3)ʳ - 1, plot the points for chosen x-values, connect them smoothly considering the function's rapid rise, and label the graph appropriately with axes. Remember the '-1' represents a vertical shift down.
Step-by-step explanation:
How to Graph the Function f(x) = 2(3)ʳ - 1
To graph the function f(x) = 2(3)¹⁰ - 1, you need to understand that it is an exponential function. Here are the steps to graph it:
- Identify the base of the exponential function, which is 3 in this case, and the coefficient before the exponential, which is 2.
- Recognize that the '-1' is a vertical shift, moving the entire graph down by one unit.
- Choose a range of x values (for example, from -2 to 2 if you are looking for a basic sketch).
- Calculate the corresponding y values using the function. For example, f(0) = 2(3)¹⁰ - 1 = 1.
- Plot the calculated points on a coordinate plane.
- Connect the points smoothly, remembering that an exponential function rises rapidly as x increases.
- Make sure to label the axes and the graph with f(x).
- The x-axis will be an asymptote since as x becomes large negative, f(x) approaches -1 but never actually reaches it.
The graph scales depend on the range of values you are graphing. Ensure the maximum x and y values are noted on the axes for clarity..