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Graph the function f(x)=2(3)ˣ −1

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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:

  1. Identify the base of the exponential function, which is 3 in this case, and the coefficient before the exponential, which is 2.
  2. Recognize that the '-1' is a vertical shift, moving the entire graph down by one unit.
  3. Choose a range of x values (for example, from -2 to 2 if you are looking for a basic sketch).
  4. Calculate the corresponding y values using the function. For example, f(0) = 2(3)¹⁰ - 1 = 1.
  5. Plot the calculated points on a coordinate plane.
  6. Connect the points smoothly, remembering that an exponential function rises rapidly as x increases.
  7. Make sure to label the axes and the graph with f(x).
  8. 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..

User Aleksandra
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