Explanation:
a) Domain of both functions is all real numbers (-∞, +∞), as there are no restrictions on the input (x).
b) The range of A) f(x)=x² /3 is [0, +∞), as the minimum value of the function is 0 and there is no maximum value.
The range of B) f(x) = -3x² is (-∞, 0], as the maximum value of the function is 0 and there is no minimum value.
c) The vertex of A) f(x)=x² /3 is at (0,0).
The vertex of B) f(x) = -3x² is at (0,0).
d) The axis of symmetry of both functions is the vertical line passing through the vertex, which is x = 0.
e) The minimum value of A) f(x)=x² /3 is 0, which occurs at the vertex.
f) The maximum value of B) f(x) = -3x² is 0, which occurs at the vertex.
g) A) f(x)=x² /3 is a horizontally shrunk version of the parent function f(x) = x² by a factor of 1/3.
B) f(x) = -3x² is a vertically stretched version of the parent function f(x) = x² by a factor of 3.
h) A) f(x)=x² /3 opens upward, as the coefficient of x² is positive.
B) f(x) = -3x² opens downward, as the coefficient of x² is negative.