To find the translated function \( Y = f(x + 5) \), we need to understand that this translation shifts the original function to the left by 5 units.
Given your original function values are:
- \( x = -2 \)
- \( x = -1 \)
- \( x = 0 \)
- \( x = 1 \)
- \( x = 2 \)
We will translate each \( x \) value in the original function by applying the transformation \( x' = x + 5 \).
This gives us the new \( x' \) values as follows:
- For \( x = -2 \), \( x' = -2 + 5 = 3 \)
- For \( x = -1 \), \( x' = -1 + 5 = 4 \)
- For \( x = 0 \), \( x' = 0 + 5 = 5 \)
- For \( x = 1 \), \( x' = 1 + 5 = 6 \)
- For \( x = 2 \), \( x' = 2 + 5 = 7 \)
Thus, the new values of \( x' \) for the translated function \( Y = f(x + 5) \) are:
- \( x' = 3 \)
- \( x' = 4 \)
- \( x' = 5 \)
- \( x' = 6 \)
- \( x' = 7 \)
Keep in mind that without the specific function \( f \) or its values at these points, we can only provide the new \( x' \) values corresponding to the original \( x \) values under the transformation. If you need the corresponding \( Y \) values for \( Y = f(x + 5) \), please provide the outputs of the original function for the given \( x \) values.