Understanding the Function f(x)=x³: Explained Step-by-Step with Graph Analysis

f(x)=x³

To understand the function f(x)=x³, let’s break it down step by step:

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To understand the function f(x)=x³, let’s break it down step by step:

1. The “f(x)” notation simply means that the function is denoted as f and it is a function of the variable x. In other words, whatever value we put in for x, we will get an output value from the function f.

2. The function f(x)=x³ is an example of a polynomial function. The exponent, in this case, is 3.

3. The “³” is called the exponent or power. It indicates that whatever value we input for x, we need to cube it or raise it to the power of 3.

4. To evaluate the function for a specific value of x, you would substitute that value into the function. For example, if we want to find f(2), we would substitute x=2 into the function: f(2) = 2³ = 2 * 2 * 2 = 8.

5. The function produces a graph that is a curve called a cubic curve. It starts from the origin (0,0) and extends infinitely in both positive and negative directions.

6. The graph of f(x)=x³ is symmetric about the origin, which means that if we reflect any point on the graph over the origin, we will find another point on the graph.

7. For large positive values of x, the function f(x)=x³ increases rapidly. For large negative values of x, the function decreases rapidly. The graph approaches negative infinity as x approaches negative infinity and positive infinity as x approaches positive infinity.

8. For x=0, the function f(0)=0³=0. So, the graph intersects the y-axis at the point (0,0).

Overall, the function f(x)=x³ is a polynomial function with an exponent of 3. It shows how the input values of x are cubed to produce the output values. Its graph is symmetric, increasing rapidly for large positive values of x and decreasing rapidly for large negative values of x.

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