f(x)=−|x−3|+1 stems from the more basic function g(x) = |x|.
The graph of this function g(x) has a v-shape with vertex at (0,0).
If you put a - sign in front of |x|, this has the effect of inverting the graph. It's still a v-shape, but it opens down. Vertex still at (0,0).
Now if you rewrite -|x| as -|x-3|, your graph will have to be moved 3 units to the RIGHT.
Finally, if you add 1 to -|x-3|, the effect on the graph immediately above is to move the whole thing upward by 1 unit.
Can you now select the correct answer?
