Given the function y = 2|x - 3| + 5, describe the transformations from the parent function y=|x|. Select all that apply.(1 point)

Question

Responses

up 5 units
up 5 units

right 3 units
right 3 units

down 5 units
down 5 units

vertical compression by 2
vertical compression by 2

left 3 units
left 3 units

vertical stretch by 2
vertical stretch by 2

reflection over the y-axis

Answer 1

The function \( y = 2|x - 3| + 5 \) can be analyzed to determine the transformations from the parent function \( y = |x| \).

1. Horizontal Shift: The term \( (x - 3) \) indicates a shift to the right by 3 units.

2. Vertical Stretch: The coefficient \( 2 \) in front of the absolute value indicates a vertical stretch by a factor of 2.

3. Vertical Shift: The \( + 5 \) indicates an upward shift of the graph by 5 units.

Now let's evaluate each option:

• Up 5 units: Yes, this applies.
• Right 3 units: Yes, this applies.
• Down 5 units: No, this does not apply.
• Vertical compression by 2: No, this does not apply.
• Left 3 units: No, this does not apply.
• Vertical stretch by 2: Yes, this applies.
• Reflection over the y-axis: No, this does not apply.

Summary of transformations:

Responses to select:

• Up 5 units
• Right 3 units
• Vertical stretch by 2