In this article, we will see a step by step explanation of how to draw the graph of the function y=x^3.
Step 1: Evaluate the function y=x^3 at some values of x.
For example when x=-2 we find the value of the function to be y = x^3 = (-2)^3 = -8.
The values taken by the function at some values of x are expressed in tabular form as follows,
|x||y=x^3||Point = (x,y)|
|-3||(-3)^3 = -27||(-3,-27)|
|-2||(-2)^3 = -8||(-2,-8)|
|-1||(-1)^3 = -1||(-1,-1)|
|0||(0)^3 = 0||(0,0)|
|1||(1)^3 = 1||(1,1)|
|2||(2)^3 = 8||(2,8)|
|3||(3)^3 = 27||(3,27)|
Step 2: Plot the points seen in the last column of the above table in order to draw the x^3 graph.
For example, to plot the point (2,8) we go 2 steps to the right on the x-axis and 8 steps above on the y-axis.
Similarly, we plot all of the points in the above table as follows:
Step 3: Join the plotted points smoothly by freehand and extend the graph to infinity above and below.
The x^3 graph looks like,
Some properties of the graph of the function y=x^3:
- The graph of the function is symmetric about the origin.
- The graph tends towards infinity as we go to the right and towards minus infinity as we go towards the left. This means the graph rises sharply as we go to the right of the origin and falls sharply as we go to the left of the origin.
- The graph has an inflection point at the origin. This means that the curvature of the graph changes at the point (0,0).
- The graph meets the x-axis at only one point which is the origin.
- The graph does not have a local maxima or a local minima.
- The graph of any general cubic function looks somewhat similar to the x^3 graph. If the function has three distinct zeroes then it meets the x-axis at three distinct points. The general cubic function also tends asymptotically towards infinity on the right and to minus infinity on the left.