Question

Write an equation for each translation of y = |x|.

2.5 units left



y = | x + 2.5 |


y = | x – 2.5 |


y = | x | + 2.5


y = | x | – 2.5

Answer 1

To translate the equation \( y = |x| \) by 2.5 units to the left, you need to replace \( x \) with \( x + 2.5 \). This is because shifting a function to the left involves adding a value to the variable \( x \).

So, the correct equation for the translation of \( y = |x| \) 2.5 units to the left is:

\[ y = |x + 2.5| \]

Hence, among the provided options:
- **Correct:** \( y = | x + 2.5 | \)
- Incorrect options include \( y = | x - 2.5 | \), \( y = | x | + 2.5 \), and \( y = | x | - 2.5 \), as they represent different transformations.