To graph the function \( y = f(x + 2) \), follow these steps:

### 1. **Understand the Transformation**:
   - The given function \( y = f(x + 2) \) is a horizontal shift of the function \( y = f(x) \).
   - The \( +2 \) inside the function causes a shift to the **left** by 2 units. This is because you subtract 2 from the \( x \)-value of every point on the graph of \( y = f(x) \) to get the corresponding point on \( y = f(x + 2) \).

### 2. **Plotting the Graph**:
   - Start with the graph of the original function \( y = f(x) \).
   - Shift each point on this graph 2 units to the left to obtain the graph of \( y = f(x + 2) \).

### 3. **Example**:
   - Suppose the original function is \( y = f(x) = x^2 \). The graph is a parabola centered at the origin \((0, 0)\).
   - To graph \( y = f(x + 2) = (x + 2)^2 \), shift the entire parabola left by 2 units. The new vertex will be at \((-2, 0)\).

### 4. **Sketching the Graph**:
   - **Original Graph ( \( y = f(x) \) )**: Sketch this first if you have the function.
   - **Shift Left**: Move every point on the original graph 2 units to the left.
  
Would you like a specific example plotted or further details on any step?

### 5 Related Questions:
1. How would the graph change if it were \( y = f(x - 2) \) instead?
2. What effect does a vertical shift have, such as \( y = f(x) + 2 \)?
3. How would you graph \( y = -f(x + 2) \)?
4. Can you explain how to combine horizontal and vertical shifts in a graph?
5. How does the graph of \( y = f(2x + 4) \) compare to \( y = f(x + 2) \)?

**Tip:** Always check if the function's transformation involves multiple operations (e.g., stretching, reflecting) to ensure accurate graphing.

Learn how to graph the function y = f(x + 2) step-by-step with this detailed guide. Understand the concept of horizontal shifts in functions and apply it to graph transformations. Suitable for high school students and anyone interested in understanding function transformations.

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