Which of the following accurately lists all discontinuities of the given function? f of x equals enlarged left-brace first row 4 comma x less than negative 4. Second row open paren x plus 2 closed paren squared comma negative 4 less than or equal to x less than or equal to negative 2. Third row negative one half x plus 1 comma negative 2 less than x less than 4. Fourth row negative 1 comma x greater than 4.

At x = −4, the left-hand value approaches 4 and the quadratic piece also equals 4, so the function is continuous there. At x = −2, the quadratic piece approaches 0 while the linear piece approaches 2, giving a jump discontinuity. At x = 4, both neighboring pieces approach −1, but the function is undefined at 4, so there is a point discontinuity. Thus the correct choice is B: a point discontinuity at x = 4 and a jump discontinuity at x = −2.

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