Alright, let's solve the problem step-by-step.
We start with the parent function [tex]\( F(x) = \sqrt{x} \)[/tex].
### Step 1: Shift Six Units Left
To shift the function six units to the left, you replace [tex]\( x \)[/tex] with [tex]\( x + 6 \)[/tex]. This yields a new function:
[tex]\[ F(x) = \sqrt{x + 6} \][/tex]
### Step 2: Shift Eleven Units Up
To shift the function eleven units up, you add 11 to the whole function. Hence, the function becomes:
[tex]\[ G(x) = \sqrt{x + 6} + 11 \][/tex]
Therefore, the new equation after applying both transformations is:
[tex]\[ G(x) = \sqrt{x + 6} + 11 \][/tex]
Thus, the correct answer is:
C. [tex]\( G(x) = \sqrt{x + 6} + 11 \)[/tex]
