Final answer:
Transform f(x)=(x-7)^3 with a horizontal shift right by 7 units and g(x)=-(x+7)^3 with a horizontal shift left by 7 units and a reflection across the x-axis. These transformations change the location and orientation of the cubic functions but do not make them even or odd functions.
Step-by-step explanation:
To transform the functions f(x) = (x-7)^3 and g(x) = -(x+7)^3, we can apply the principles of transformations of functions. For f(x), the subtraction of 7 from x in the parentheses indicates a horizontal shift 7 units to the right. The cubic term means the graph will look like a normal cubic function, with the inflection point occurring at (7,0) after the shift.
For g(x), the negative sign in front of the function reflects it across the x-axis, while the addition of 7 to x in the parentheses results in a horizontal shift 7 units to the left. Again, the cubic term will have the characteristic shape of a cubic function, but this time flipped over the x-axis and the inflection point will be at (-7,0).
To relate to the idea of even and odd functions, f(x) and g(x) are neither even nor odd since their reflections would not result in the original functions or the additive inverses of the functions. Even functions are symmetric about the y-axis, while odd functions exhibit symmetry when reflected about the origin (both the x and y axes).