Use graphing technology to find the range of the function f, of, x, equals, vertical bar, x, plus, 4, vertical bar, plus, 2, .f(x)=∣x+4∣+2.

The graph of \( f(x) = |x + 4| + 2 \) shows that the function reaches a minimum value of 2 at \( x = -4 \). Since the function is based on an absolute value, it increases in both directions away from this point.

### Range of the Function:
- **Minimum value:** \( f(-4) = 2 \).
- **As \( x \to \infty \) or \( x \to -\infty \)**, \( f(x) \) increases without bound.

Thus, the **range** of the function is:
\[
\boxed{[2, \infty)}
\]

Would you like further explanation or analysis?  

### 5 Related Questions:
1. What is the domain of \( f(x) = |x + 4| + 2 \)?
2. How do we find the vertex of an absolute value function?
3. What transformations occur between \( f(x) = |x| \) and \( f(x) = |x + 4| + 2 \)?
4. How does the range change if the equation were \( f(x) = |x + 4| - 1 \)?
5. Can we rewrite absolute value functions as piecewise functions?

**Tip:** Absolute value functions always have a V-shaped graph, and their range is determined by their lowest point (if it exists).

Use graphing technology to find the range of the function f(x) = |x + 4| + 2.

Learn how to determine the range of the function f(x) = |x + 4| + 2 using graphing technology. Explore key algebraic concepts, including properties of absolute value functions and graph analysis, with a focus on identifying the function's minimum value and understanding its behavior as x increases or decreases. Suitable for students in Grades 9-11.

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