Notice that the given graph is the graph of the function g(x)=|x| reflected over the x-axis, translated 1 unit to the right, and translated 1 unit up.
Now, recall that:
1) The function represented by the graph of the function h(x) reflected over the x-axis is:
[tex]-h(x)\text{.}[/tex]2) The function represented by the graph of the function h(x) translated n units to the right is:
[tex]h(x-n)\text{.}[/tex]3) The function represented by the graph of the function h(x) translated m units up is:
[tex]h(x)+m[/tex]Therefore, the function that is represented by the graph of g(x)=|x| reflected over the x-axis, translated 1 unit to the right, and then translated 1 unit up is:
[tex]f(x)=-|x-1|+1.[/tex]Answer: Second option.