Question

The range of the function $f(x)=\sqrt{x^{2}+4x+4}$ is:

• A. [0, $\infty$)
• B. [1, $\infty$)
• C. [3, $\infty$)
• D. [2, $\infty$)
• E. [4, $\infty$)

Hint:

The output of a principal square root function is always non-negative.

Answer 1

The Correct Option is A

Step 1: Concept
Simplify the expression under the square root.

Step 2: Analysis
Observe that $x^2 + 4x + 4 = (x + 2)^2$. Thus, $f(x) = \sqrt{(x+2)^2} = |x+2|$.

Step 3: Conclusion
The absolute value function $|x+2|$ always results in values $\ge 0$. Hence, the range is $[0, \infty)$. Final Answer: (A)