Answer:
Option B: [tex]y=\left \{ {{x^2+6,x<3} \atop {-x+6,x\geq3}} \right.[/tex]
Step-by-step explanation:
We can see that the first part of the piecewise function is a parabola with a y-intercept of (0,6) where the domain is restricted for all values of x less than 3 given the open circle at x=3.
The second part of the piecewise function is a linear function with a negative slope where the domain is restricted for all values of x greater than or equal to 3 given the closed circle at x=3.
Essentially, the piecewise function has a jump discontinuity at x=3 where the first part of the function goes to the second part of the function at one point by "jumping".
