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).