Answer:
Option C is correct.
Explanation:
We are given a graph of piece-wise function which break at x=1
We need to choose correct option for graph.
Function is break at x=1.
We will get two function
For x≤1 and x>1
As we can see x≤1, graph is linear and x>1 graph is parabolic.
Equation of linear graph, x≤1
Take two point of graph (0,6) and (-6,0)
Equation of line: [tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y=1(x+6)[/tex]
f(x)=x+6 , x≤1
Equation of parabolic graph, x>1
[tex]f(x)=x^2+3[/tex]
Piece-wise function
[tex]f(x)=\left\{\begin{matrix}x^2+3&\ \ \text{ If }x>1\\x+6&\ \ \text{ If }x\leq 1\end{matrix}\right[/tex]
Please see the attached figure.
Hence, The option C is correct.
