y =2|x-3| is a function that was transformed from it’s parent function what is the parent function

Question

y =x
y =|x|
y = |x-3|
y = 2x-3

Answer 1

The function \( y = 2|x - 3| \) is a transformation of the parent function \( y = |x| \).

Here's a breakdown of how the transformations work:

1. The absolute value function: The parent function is \( y = |x| \).
2. The transformation:
   • The expression \( |x - 3| \) indicates a horizontal shift to the right by 3 units.
   • The coefficient 2 indicates a vertical stretch by a factor of 2.

So the parent function for your transformed function \( y = 2|x - 3| \) is \( y = |x| \).

Therefore, the correct answer is \( y = |x| \).