Master the Basics of Graphing Cubic Functions: A Step-by-Step Guide

y = ​x​ cubed

Let’s work through this math problem step by step to understand the concept of polynomial functions and how to graph them

Let’s work through this math problem step by step to understand the concept of polynomial functions and how to graph them.

The equation y = x cubed is an example of a polynomial function. In this case, it is a cubic function because the highest power of x is 3.

To graph this function, you can create a table of values by choosing different x-values and calculating the corresponding y-values. Let’s start with some x-values and find their y-values.

For example, let’s pick x = -2, -1, 0, 1, and 2.

When x = -2, we have y = (-2)^3 = -8.
When x = -1, we have y = (-1)^3 = -1.
When x = 0, we have y = (0)^3 = 0.
When x = 1, we have y = (1)^3 = 1.
When x = 2, we have y = (2)^3 = 8.

Now, we can use these values to plot points on a graph. The x-values go on the horizontal axis (x-axis) and the corresponding y-values go on the vertical axis (y-axis).

When x = -2, y = -8, which gives us the point (-2, -8).
When x = -1, y = -1, which gives us the point (-1, -1).
When x = 0, y = 0, which gives us the point (0, 0).
When x = 1, y = 1, which gives us the point (1, 1).
When x = 2, y = 8, which gives us the point (2, 8).

Now, we can connect these points on the graph to visualize the shape of the function. In this case, the graph of y = x^3 is a curve that passes through the points (-2, -8), (-1, -1), (0, 0), (1, 1), and (2, 8).

Please note that this is just a basic introduction to graphing the cubic function y = x^3. As you study more about polynomials, you will learn additional techniques for analyzing and graphing more complex functions.

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