Which transformations have been performed on the graph of to obtain
the graph of ?
Select each correct answer.
Select 2 correct answer(s)
The function is translated 2 units right.
The function is translated 4 units right.
The function is translated 2 units up.
The function is translated 4 units down.

Ask by Mullins Stanley. in the United States

Jan 17,2025

Question

Which transformations have been performed on the graph of to obtain
the graph of ?
Select each correct answer.
Select 2 correct answer(s)
The function is translated 2 units right.
The function is translated 4 units right.
The function is translated 2 units up.
The function is translated 4 units down.

Ask by Mullins Stanley. in the United States

Jan 17,2025

UpStudy AI · Accepted Answer

To determine the transformations applied to the graph of $$ f(x) = \sqrt{x} $$ to obtain $$ g(x) = \sqrt{x-4} + 2 $$, let's analyze each part of the function $$ g(x) $$:

1. **Horizontal Shift**:
   - The expression $$ \sqrt{x - 4} $$ indicates a horizontal shift.
   - The term $$ x - 4 $$ inside the square root means the graph of $$ f(x) = \sqrt{x} $$ is shifted **4 units to the right**.

2. **Vertical Shift**:
   - The $$ +2 $$ outside the square root indicates a vertical shift.
   - This means the graph is shifted **2 units upward**.

Therefore, the transformations applied are:
- **Translated 4 units right**
- **Translated 2 units up**

**Correct Answers**:
- The function is translated 4 units right.
- The function is translated 2 units up.
The graph of $$ g(x) = \sqrt{x-4} + 2 $$ is obtained by translating the graph of $$ f(x) = \sqrt{x} $$ **4 units to the right** and **2 units up**.

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