Question
Find the function that is finally graphed after the following transformations are applied to the graph of \( y=\sqrt{x} \) in the order listed. (1) Reflect about the x-axis (2) Shift down 6 units (3) Shift left 2 units \( y=\square \)
Ask by Coles Salazar. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The final function after all transformations is \( y = -\sqrt{x + 2} - 6 \).
Solution
Starting with the function y = √x, we apply each transformation step-by-step:
1. Reflect about the x-axis:
Replace √x with –√x.
New function: y = –√x.
2. Shift down 6 units:
Subtract 6 from the function.
New function: y = –√x – 6.
3. Shift left 2 units:
Replace x with x + 2 (since shifting left by 2 corresponds to using (x+2) inside the function).
Final function: y = –√(x + 2) – 6.
Thus, the final transformed function is:
y = −√(x + 2) − 6.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To find the final function after these transformations, we start with the base function \( y = \sqrt{x} \). 1. **Reflect about the x-axis**: This changes the function to \( y = -\sqrt{x} \). 2. **Shift down 6 units**: We subtract 6 from the entire function, resulting in \( y = -\sqrt{x} - 6 \). 3. **Shift left 2 units**: Replacing \( x \) with \( x + 2 \) shifts the graph left. Thus, we get \( y = -\sqrt{x + 2} - 6 \). Combining all transformations, the final function graphed is: \[ y = -\sqrt{x + 2} - 6 \]
