Final answer:
The student's question is about calculating values for a piecewise function k(x) for different intervals of x. The function is -2x - 1 for x ≤ -4, and 2x² + 6x - 5 for -4 < x ≤ 5.
Step-by-step explanation:
The student has asked for the calculation of specific values for a piecewise function k(x). The function is defined differently for different intervals of x values. More specifically, the function is defined as k(x) = -2x - 1 for x ≤ -4, and as k(x) = 2x² + 6x - 5 for -4 < x ≤ 5. To calculate the values for x within these intervals, one would use the corresponding function expression.
For example, if we need to calculate k(-5), since -5 ≤ -4, we use the first expression and get k(-5) = -2(-5) - 1 = 10 - 1 = 9.
If we need to calculate k(0), since -4 < 0 ≤ 5, we use the second expression and get k(0) = 2(0)² + 6(0) - 5 = -5.