Answer:
Yes, the graph represents the piecewise function.
Step-by-step 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 [tex]2\leq x<4[/tex], so
[tex]f(x)=5 \text{ for }2\leq x<4[/tex]
The vertex of the parabola is (0,0) and the other point on the parabola is (-2,4).
So the equation of parabola is,
[tex]y=a(x-h)^2+k[/tex]
Where (h,k) is vertex.
[tex]y=a(x)^2[/tex]
Since (-2,4) lies on parabola.
[tex]4=a(-2)^2[/tex]
[tex]a=1[/tex]
So, the equation of parabola is [tex]y=x^2[/tex]. Since the function is parabolic before x=2,
[tex]f(x)=x^2\text{ for }x<2[/tex]
[tex]f(x)=\begin{cases}x^2 & \text{ if } x<2 \\ 5 & \text{ if } 2\leq x<4\end{cases}[/tex]
Therefore the graph is a piecewise function.
