Final answer:
To determine the values of a piecewise function f(x) for different x values, we must identify the interval that x falls within and apply the corresponding rule for that interval to calculate f(x).
Step-by-step explanation:
To answer the student's schoolwork question about identifying the values of f(x) for different x values in a piecewise function, we must examine each specified interval and apply the function rule that corresponds to that range of x values.
For example, in option a), we have f(x) = 8 when x = -1, f(x) = 2x when -1 < x ≤ 4, and f(x) = -4 - x when x > 4. If x equals -1, then f(x) is simply 8. If x is between -1 and 4 (not including -1), we calculate f(x) by doubling the value of x. For x values greater than 4, f(x) is found by subtracting the value of x from -4.
Similar logic applies to options b), c), and d). In each case, we must first identify the interval to which the x value belongs, and then apply the corresponding rule to find the correct value of f(x).