For given the following piecewise function find the domain and range

F(x) ={ 2x + 4 for x< -3}
{-1 for -3-¡Ü x ¡Ü4}
{- x 1 for x > 4}

To find the domain and range of a piecewise function, we need to consider three cases:

Case 1: x < -3
For x < -3, the function F(x) is defined as 2x + 4. In this case, there are no restrictions on x, so the domain is (-∞, -3). The range of F(x) is all real numbers since there are no restrictions on the output values.

Case 2: -3 ≤ x ≤ 4
For -3 ≤ x ≤ 4, the function F(x) is defined as -1. In this case, the domain is [-3, 4] since x is limited to this interval. The range of F(x) is just -1, as this is the only possible output value.

Case 3: x > 4
For x > 4, the function F(x) is defined as -x + 1. Here, the domain is (4, ∞) because x is restricted to values greater than 4. The range of F(x) is all real numbers since there are no restrictions on the output values.

Combining all three cases, the domain of the function F(x) is (-∞, -3] ∪ [4, ∞) and the range is all real numbers except for -x - 1 for -3 ≤ x ≤ 4.