Rational Number

The given function is: Step 1: Completing the square to rewrite the quadratic expression.
First, we complete the square for the quadratic expression .
Factor out the coefficient of from the first two terms:
Now, complete the square inside the parentheses.
The coefficient of is , so half of it is , and squaring it gives . Add and subtract inside the parentheses: Simplify:
Step 2: Determine the range.
Since the expression inside the square root is always non-negative for all real values of , the minimum value of the function occurs when , i.e., when . At , the value of is: Therefore, the range of the function is: Thus, the correct answer is (C).