Question

Consider the function .

The piecewise functions that coincide with the given function are and .

Answer 1

Explanation:

If the graph divide into two pieces that it is a piecewise function. Since the given graph is available in two ices therefore it is a piecewise function.

From the graph it is noticed that the function is parabolic before x=2 and after that the function have constant value 5 from x=2 to x=4 excluding 4.

Since the value of the function is constant for , so

The vertex of the parabola is (0,0) and the other point on the parabola is (-2,4).

So the equation of parabola is,

Where (h,k) is vertex.

Since (-2,4) lies on parabola.

So, the equation of parabola is . Since the function is parabolic before x=2,

Therefore the graph is a piecewise function

Answer 2

Yes, the graph represents the piecewise function.

Explanation:

If the graph divide into two pieces that it is a piecewise function. Since the given graph is available in two ices therefore it is a piecewise function.

From the graph it is noticed that the function is parabolic before x=2 and after that the function have constant value 5 from x=2 to x=4 excluding 4.

Since the value of the function is constant for , so

The vertex of the parabola is (0,0) and the other point on the parabola is (-2,4).

So the equation of parabola is,

Where (h,k) is vertex.

Since (-2,4) lies on parabola.

So, the equation of parabola is . Since the function is parabolic before x=2,

Therefore the graph is a piecewise function