Question

what does the transformation f(x)↦f(x+8) do to the graph of f(x)

translates it 8 units left and 2 units down
translates it 8 units right and 2 units down
translates it 8 units right and 2 units up
translates it 8 units left and 2 units up

Answer 1

The transformation \( f(x) \mapsto f(x+8) \) translates the graph of \( f(x) \) horizontally. Specifically, it shifts the graph to the left by 8 units.

To clarify: in general, for a function \( f(x) \):
- \( f(x + c) \) translates the graph **c units to the left** if \( c \) is positive.
- \( f(x - c) \) translates the graph **c units to the right** if \( c \) is positive.

So, in this case, \( f(x) \mapsto f(x+8) \) translates the graph of \( f(x) \) 8 units to the left. None of the options provided mention a downward or upward shift, so it's clear that the shift is purely horizontal.

Thus, none of the given choices are correct because they all include vertical translations. The correct interpretation is:

- Translates it 8 units left (and does not involve any vertical shift).