Let's analyze the question.

The given function is:

$f(x) = |x| + 2$

You are tasked with determining whether $f(-2) = 0$ is true or false.

Step 1: Evaluate $f(-2)$

Substitute $x = -2$ into the function:

$f(-2) = |-2| + 2$

The absolute value of $-2$ is $2$. So:

$f(-2) = 2 + 2 = 4$

Step 2: Check if $f(-2) = 0$

Clearly, $f(-2) = 4$, which is not equal to 0.

Conclusion:

The statement $f(-2) = 0$ is false.

Let me know if you'd like a detailed explanation or have any follow-up questions! Here are some related questions to consider:

1. What is the range of the function $f(x) = |x| + 2$?
2. How does the absolute value function influence the graph of $f(x)$?
3. What are the x-values that make $f(x) = 4$?
4. Can $f(x) = 0$ for any real $x$?
5. How would the function change if $f(x) = |x| - 2$?

Tip: When working with absolute value functions, always simplify the absolute value expression before applying further operations!