Question

Write the equation of the piecewise function whose graph is shown

Answer 1

C

Explanation:

Answer 2

1. The intevals of x should be:

• 
  `x\le -1,` because point (-1,1) lies on the linear part of the graph;
• 
  `-1<x\le 3,` because the point (-1,1) doesn't lie on the first parabola;
• 
  `x>3.`

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.