Final answer:
To evaluate the piecewise function f(x), apply the appropriate rule based on the given x value. For x=0 and x=1, use f(x) = 3x - 5; for x=2, which is on the boundary, still use f(x) = 3x - 5; for x=6, use f(x)=x³ - 2.
Step-by-step explanation:
The question deals with evaluating a piecewise function where different rules apply to different intervals of x. In the student's case, the function f(x) is described by f(x) = 3x - 5 for -3 ≤ x ≤ 2, and f(x) = x³ - 2 for x > 2.
- f(0) falls in the first interval (-3 to 2), so we apply the first function rule: f(0) = 3(0) - 5 = -5.
- f(1) also falls in the first interval, thus: f(1) = 3(1) - 5 = -2.
- f(2) is at the boundary of the intervals. Since the inequality for the first function includes the point where x = 2, we use the first function rule: f(2) = 3(2) - 5 = 1.
- Since f(6) is greater than 2, we use the second function rule: f(6) = 6³ - 2 = 216 - 2 = 214.