what does the transformation f(x)↦f(x+1) do to the graph of f(x)

Question

translates it 1 unit left and 1 unit down
translates it 1 unit right and 1 unit up
translates it 1 unit right and 1 unit down
translates it 1 unit left and 1 unit up

Answer 1

The transformation $f(x)\mapsto f(x+1)$ translates the graph of the function $f(x)$ 1 unit to the left.

Here's why:

• The expression $f(x+1)$ implies that for each $x$ value on the original graph, the output corresponds to the input $x+1$. This means to get the same output as $f(x)$ at point $x$, you need to input $x+1$.
• Therefore, in order to map the output of $f(x)$ to a value that is at the original position, we must move the point where it's being evaluated by one unit to the left.

So the correct answer is: translates it 1 unit left and 1 unit up.