Answered

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If you apply the below transformations to the square root parent function, [tex][tex]$F(x)=\sqrt{x}$[/tex][/tex], what is the equation of the new function?
- Shift six units left.
- Shift 11 units up.

A. [tex][tex]$G(x)=\sqrt{x-6}+11$[/tex][/tex]

B. [tex][tex]$G(x)=\sqrt{x+11}+6$[/tex][/tex]

C. [tex][tex]$G(x)=\sqrt{x+6}+11$[/tex][/tex]

D. [tex][tex]$G(x)=\sqrt{x+11}-6$[/tex][/tex]

Sagot :

GinnyAnswer
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]
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