$$  $$Graph the function f(x)=X^3 +3 X^2 +2

To graph the function $ f(x) = x^3 + 3x^2 + 2 $, let's go through the steps:

### 1. Identify the basic characteristics of the function:
- **Degree**: The function is a cubic polynomial, meaning it has degree 3.
- **Leading Coefficient**: The coefficient of $ x^3 $ is positive, so the graph will rise to the right and fall to the left.
- **Intercepts**: Let's find the $ y $-intercept and the $ x $-intercepts.

### 2. Calculate the intercepts:
- **Y-intercept**: Set $ x = 0 $.
  \[
  f(0) = 0^3 + 3(0)^2 + 2 = 2
  \]
  So, the $ y $-intercept is $ (0, 2) $.

- **X-intercepts**: Solve $ f(x) = 0 $.
  \[
  x^3 + 3x^2 + 2 = 0
  \]
  This can be solved either by factoring or using numerical methods.

### 3. Determine

Learn how to graph the cubic polynomial function f(x) = x^3 + 3x^2 + 2 step-by-step with detailed instructions. This problem covers polynomial functions, intercepts calculation, and graphing techniques. Suitable for high school students.

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