Answer:
The correct option is A.
Step-by-step explanation:
From the given graph it is clear that the graph it divided in two pieces, so it is piece-wise function.
We have two different function one is for x≥2 and another is for x<2 because we have an open circle on x=2.
From the graph it is clear that the function is linear for x≥2 and it is directly proportional to x.
[tex]F(x)=x[/tex] for x≥2
This function is represent by only option A. The function of option A is
[tex]f(x)=\begin{cases}|4-x^2| & \text{ if } x<2 \\ x & \text{ if } x\geq 2 \end{cases}[/tex]
From the given graph it is clear that the y-intercept of the graph is 4.
The y-intercept of F(x) in option A is
[tex]|4-(0)^2|=4[/tex]
Therefore the correct option is A.
