Question

Write the equation of the piecewise function whose graph is shown

Answer 1

1. The intevals of x should be:

• $x\le -1,$ because point (-1,1) lies on the linear part of the graph;
• $-1$ 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.