To graph the exponential function y = 3^x, follow these steps:
- Create a Table of Values: Start by choosing a range of x values. For example, you might select -2, -1, 0, 1, and 2. Calculate the corresponding y values using the function:
- x = -2: y = 3^(-2) = 1/9 ≈ 0.11
- x = -1: y = 3^(-1) = 1/3 ≈ 0.33
- x = 0: y = 3^0 = 1
- x = 1: y = 3^1 = 3
- x = 2: y = 3^2 = 9
- Plot the Points: Use the calculated (x, y) pairs: (-2, 0.11), (-1, 0.33), (0, 1), (1, 3), and (2, 9). Plot these points on a graph.
- Draw the Curve: The graph of y = 3^x will be a smooth curve that rises steeply as x increases and approaches the x-axis but never touches it as x becomes more negative. It crosses the y-axis at (0, 1).
- Label the Axes: Make sure to label your x and y axes and give an appropriate title to your graph.
This graph illustrates the characteristic shape of exponential functions, emphasizing rapid growth for positive values and approaching zero for negative values.