The Power of Three: Understanding the Cubing Function and Its Properties

Cubing Function

The cubing function is a mathematical function that raises a number to the power of 3

The cubing function is a mathematical function that raises a number to the power of 3. It is represented by the equation f(x) = x^3, where f(x) denotes the value of the function at x.

To understand how the cubing function works, let’s consider a few examples:

Example 1:
If we substitute x = 2 into the equation f(x) = x^3, we get f(2) = 2^3 = 8. This means that when we cube the number 2, we obtain the result 8.

Example 2:
Similarly, if we substitute x = -3 into the equation, we get f(-3) = (-3)^3 = -27. Therefore, when we cube the number -3, the result is -27.

Example 3:
Let’s consider x = 0. Substituting x = 0 into the equation, we get f(0) = 0^3 = 0. Hence, when we cube the number 0, the result is also 0.

From these examples, we can observe that the cubing function has the following properties:
1. When the input number is positive, the output is positive.
2. When the input number is negative, the output is negative.
3. When the input number is 0, the output is also 0.

The cubing function is a polynomial function with a degree of 3, and its graph has a distinctive shape. It starts from the bottom left and extends towards the top right quadrants, passing through the origin (0,0). It has a steep incline for positive x-values and a steep decline for negative x-values.

In summary, the cubing function raises the input number to the power of 3, resulting in a positive or negative output depending on the sign of the input number. Understanding the properties and graph of the cubing function can be useful in various mathematical applications.

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