Final answer:
To transform the function g(x) = 0.25(x-7)^3 - 2 by translating 14 units left and 7 units down, we replace x with (x + 14) and subtract 7 from the whole expression to get g(x) = 0.25(x + 7)^3 - 9.
Step-by-step explanation:
To find the expression for g(x) after a translation of 14 units left and 7 units down, we need to adjust the given function g(x) = 0.25(x−7)3 −2. A translation of 14 units left means we will replace x with x + 14. A translation of 7 units down means we will subtract 7 from the entire original function.
The transformed function, therefore, is: g(x) = 0.25((x + 14) - 7)3 - 2 - 7. Simplifying this expression gives us: g(x) = 0.25(x + 7)3 - 9.