1. The intevals of x should be:
- [tex]x\le -1,[/tex] because point (-1,1) lies on the linear part of the graph;
- [tex]-1<x\le 3,[/tex] because the point (-1,1) doesn't lie on the first parabola;
- [tex]x>3.[/tex]
This gives you that option B is false.
Now the middle part of the graph is parabola going in negative y-direction and right part of the graph is parabola going in positive y-direction. Therefore, option A is false, because there the middle parabola is going upward.
The third part of the graph has vertex at point (5,4). In option D the vertex of the parabola is (3,4), so this option is false.
Answer: correct choice is C.
