Answer:
To graph the equation y = 2x^3, we can follow these steps:
1. Choose a range of x-values: Select a range of x-values that will cover the desired portion of the graph. For example, you might choose x-values from -3 to 3 to visualize a symmetric graph around the y-axis.
2. Substitute the x-values into the equation: Substitute each x-value into the equation to find the corresponding y-values. For example, if x = -3, substitute it into the equation: y = 2(-3)^3. Evaluate the equation to find the y-value.
3. Plot the points: Using the x and y pairs obtained from step 2, plot the points on the graph. For example, if x = -3 and y = -54, plot the point (-3, -54).
4. Repeat steps 2 and 3 for the remaining x-values: Substitute the other chosen x-values into the equation, evaluate, and plot the corresponding points.
5. Connect the points: Once you have plotted all the points, connect them smoothly to form a curve. Since the equation is y = 2x^3, the graph will likely resemble an "S" shape.
6. Label the axes and add a title: Label the x-axis and y-axis with appropriate values and units, if applicable. Also, add a title to the graph to provide a brief description of the equation or the context it represents.