Final answer:
To evaluate the various expressions for the function f(x) = 3x^2 + 4x - 3, we substitute the indicated values and simplify accordingly to find f(0), f(3), f(-3), f(-x), -f(x), f(x + 2), f(3x), and f(x + h).
Step-by-step explanation:
To answer this question, we will evaluate and transform the function f(x) = 3x2 + 4x - 3 according to the provided operations.
(a) To find f(0), substitute x with 0: f(0) = 3(0)2 + 4(0) - 3 = -3.
(b) To find f(3), substitute x with 3: f(3) = 3(3)2 + 4(3) - 3 = 27 + 12 - 3 = 36.
(c) To find f(-3), substitute x with -3: f(-3) = 3(-3)2 + 4(-3) - 3 = 27 - 12 - 3 = 12.
(d) To find f(-x), substitute x with -x: f(-x) = 3(-x)2 + 4(-x) - 3 = 3x2 - 4x - 3.
(e) To find -f(x), multiply the function by -1: -f(x) = -(3x2 + 4x - 3) = -3x2 - 4x + 3.
(f) To find f(x + 2), substitute x with (x + 2): f(x + 2) = 3(x + 2)2 + 4(x + 2) - 3.
(g) To find f(3x), substitute x with 3x: f(3x) = 3(3x)2 + 4(3x) - 3 = 27x2 + 12x - 3.
(h) To find f(x + h), substitute x with (x + h): f(x + h) = 3(x + h)2 + 4(x + h) - 3.