Question

Which of the following functions is graphed below

Answer 1

Option B:
`y=\left \{ {{x^2+6,x<3} \atop {-x+6,x\geq3}} \right.`

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".