Which of the following accurately lists all discontinuities of the function below?

Checking the discontinuity at point -4
from the left f(-4) = 4
from the right f(-4) = (-4+2)² = (-2)² = 4
∴ The function is continues at -4

Checking the discontinuity at point -2
from the left f(-2) = (-2+2)² = 0
from the right f(-2) = -(1/2)*(-2)+1 = 2
∴ The function is jump discontinues at -2

Checking the discontinuity at point 4
from the left f(4) = -(1/2)*4+1 = -1
from the right f(4) = -1
but there no equality in the equation so,
∴ The function is discontinues at 4

The correct choice is the second
point discontinuity at x = 4 and jump discontinuity at x = -2

Where’s the problems ? ?