Answer:
Plotting these points and connecting them with a curve will give you the graph of y = e^(x/2).
Explanation:
To graph the equation y = e^(x/2), which represents an exponential function, follow these steps:
1. Determine the range of values for x that you want to graph. This will depend on the specific context of the problem or the range specified.
2. Choose a set of x-values within the chosen range. For simplicity, you can select evenly spaced values. For example, you could use x = -4, -2, 0, 2, and 4.
3. Calculate the corresponding y-values by plugging each x-value into the equation y = e^(x/2). Use a calculator or software that can evaluate exponentials.
4. Plot the points (x, y) on a graph. The x-values will be on the horizontal axis, and the y-values will be on the vertical axis.
5. Connect the points with a smooth curve. Since the exponential function increases rapidly, the curve will appear to be "steep" as x values increase.
6. Extend the curve beyond the plotted points to visualize the behavior of the function outside of the chosen range.
Note: It's also important to label the axes and provide a title for the graph to provide clarity and context.
For example, if we use the x-values mentioned above, we can calculate the corresponding y-values as follows:
For x = -4: y ≈ e^(-4/2) = e^(-2) ≈ 0.135
For x = -2: y ≈ e^(-2/2) = e^(-1) ≈ 0.368
For x = 0: y = e^(0/2) = e^0 = 1
For x = 2: y ≈ e^(2/2) = e^1 ≈ 2.718
For x = 4: y ≈ e^(4/2) = e^2 ≈ 7.389
Plotting these points and connecting them with a curve will give you the graph of y = e^(x/2).