Final answer:
To graph a cubic function y=ax³, create a table of values with x-values -2, -1, 0, 1, and 2, calculate the corresponding y-values, plot the points on a graph, and draw a smooth curve through them, creating the characteristic shape of the cubic function.
Step-by-step explanation:
To graph a cubic function such as y = ax³, you can begin by choosing x-values and substituting them into the equation to find their corresponding y-values. Start with x=0, for which the value of y will also be 0, since any number raised to the power of 3 and then multiplied by a (where a is a constant) will equal 0 if x=0. Then choose two values of x greater than 0 and two values less than 0. Let's use the points -2, -1, 1, and 2 to plot along with the origin (0,0).
Creating a table of values, with one column for x and one for y, calculate the y-value for each x-value. For example, if a=1 and we've chosen the points mentioned above, our table may look like this:
- (-2, -8)
- (-1, -1)
- (0, 0)
- (1, 1)
- (2, 8)
Finally, plot these points on the Cartesian plane and draw a smooth curve through all the points, ensuring that the graph shows the characteristic shape of a cubic function, which rises and falls with no sharp corners. Remember, the exact shape will depend on the value of coefficient 'a' in the original equation.