Question

Write an equation for each translation of .

6.5 units up



y = | x | + 6.5


y + 6.5 = | x |


y = | 6.5 x |


y = | x | – 6.5

Answer 1

To achieve a translation of the function \( y = |x| \) by 6.5 units up, you would add 6.5 to the entire function. The correct equation for the translation is:

\[ y = |x| + 6.5 \]

This means that every point on the original graph of \( y = |x| \) is moved up by 6.5 units.

The other options provided can be analyzed as follows:

1. **\( y + 6.5 = |x| \)**: This is not the correct form as it suggests that \( y \) is equal to \( |x| - 6.5 \).

2. **\( y = |6.5x| \)**: This represents a different function, scaling \( x \) rather than translating upward.

3. **\( y = |x| - 6.5 \)**: This represents a downward shift of the function, moving it 6.5 units down instead of up.

Thus, the correct answer is:

\[ y = |x| + 6.5 \]