f(0) = −3 * 0 + 2 = 2
$f(\frac{2}{3}) = -3 * \frac{2}{3} + 2 = -2 + 2 = 0$
f(−3) = −3 * (−3) + 2 = 9 + 2 = 11
$f(-\frac{1}{2}) = -3 * (-\frac{1}{2}) + 2 = \frac{3}{2} + 2 = 1\frac{1}{2} + 2 = 3\frac{1}{2}$

f(−x) = −3 * (−x) + 2 = 3x + 2
−f(x) = −(−3x + 2) = 3x − 2
f(2x) = −3 * 2x + 2 = −6x + 2
f(x − 2) = −3(x − 2) + 2 = −3x + 6 + 2 = −3x + 8

$f(x^2) = -3x^2 + 2$
$(f(x))^2 = (-3x + 2)^2 = 9x^2 - 12x + 4$
$f((x - 1)^2) = -3(x - 1)^2 + 2 = -3(x^2 - 2x + 1) + 2 = -3x^2 + 6x - 3 + 2 = -3x^2 + 6x - 1$
$(f(-x^2) - 1)^2 = (-3 * (-x^2) - 1 + 2)^2 = (3x^2 + 1)^2 = 9x^4 + 6x^2 + 1$

$f(-x^3) = -3 * (-x^3) + 2 = 3x^3 + 2$
$(2x^3) = -3 * 2x^3 + 2 = -6x^3 + 2$
$f((2x)^3) = -3 * (2x)^3 + 2 = -3 * 8x^3 + 2 = -24x^3 + 2$
$(f(2x))^3 = (-3 * 2x + 2)^3 = (-6x + 2)^3 = (2 - 6x)^3$