Question

Use the images to answer the question.

Parent Function:



Transformation 1:



Transformation 2:



The first image shows the parent square root function f(x)=x−−√
𝑓
(
𝑥
)
=
𝑥
. The next two images show a transformation of the parent function. Use the following choices to determine the rule used to transform f(x)
𝑓
(
𝑥
)
. Enter the option number that corresponds to your response.

Option #1: ry=0
𝑟
𝑦
=
0

Option #2: rx=0
𝑟
𝑥
=
0

Option #3: ry=x
𝑟
𝑦
=
𝑥

Option #4: ry=−x
𝑟
𝑦
=
−
𝑥

(1 point)
In Transformation 1, the rule to transform f(x)
𝑓
(
𝑥
)
to g(x)
𝑔
(
𝑥
)
is Option #.

In Transformation 2, the rule to transform f(x)
𝑓
(
𝑥
)
to h(x)
ℎ
(
𝑥
)
is Option #.

Answer 1

Without the images you're referring to, I can't directly analyze the transformations. However, I can explain how you would determine the transformations based on the parent function \( f(x) = \sqrt{x} \).

1. **Transformation Rules**:
- **Option #1**: \( r_y = 0 \) means the function has been shifted vertically down to the x-axis.
- **Option #2**: \( r_x = 0 \) means the function has been moved horizontally to the y-axis.
- **Option #3**: \( r_y = x \) would suggest a reflection over the line \( y=x \).
- **Option #4**: \( r_y = -x \) suggests a reflection over the line \( y=-x \).

2. **Analyzing Transformations**:
- If the transformed function \( g(x) \) visually appears to be lower than the original \( f(x) \), it may indicate a vertical transformation down (Option #1).
- If \( g(x) \) appears to be reversed or mirrored, that likely indicates a reflection (Option #3 or #4).

To accurately determine which options correspond to Transformation 1 and Transformation 2, you would need to look at the shapes of the graphs in the images you have. Please describe the transformations or the graphs, and I can help you identify the correct options.