1. The problem asks to write equations of cubic functions with given zeros and belonging to the same family of functions. 2. For cubic functions with zeros $r_1$, $r_2$, and $r_3$, the general form is: $$f(x) = a(x - r_1)(x - r_2)(x - r_3)$$ where $a$ is a nonzero constant that scales the function but does not change the zeros. 3. To write three cubic functions in the same family, choose different values of $a$ (e.g., 1, 2, -1) and use the given zeros. 4. Example for question 4a) zeros: $-3$, $6$, $4$: - $f_1(x) = (x + 3)(x - 6)(x - 4)$ - $f_2(x) = 2(x + 3)(x - 6)(x - 4)$ - $f_3(x) = -1(x + 3)(x - 6)(x - 4)$ 5. Similarly, for question 4b) zeros: $5$, $-1$, $-2$: - $f_1(x) = (x - 5)(x + 1)(x + 2)$ - $f_2(x) = 3(x - 5)(x + 1)(x + 2)$ - $f_3(x) = -2(x - 5)(x + 1)(x + 2)$ 6. This method applies to all parts: write the product of linear factors for the zeros, then multiply by different constants to get three functions in the same family. 7. For question 3 (which is not explicitly stated but assuming it is similar), the process is the same: identify zeros, write the product of factors, and vary $a$. This approach ensures all functions have the same zeros but differ by a constant multiplier, thus belonging to the same family. Final answer for question 4a): $$f_1(x) = (x + 3)(x - 6)(x - 4)$$ $$f_2(x) = 2(x + 3)(x - 6)(x - 4)$$ $$f_3(x) = -1(x + 3)(x - 6)(x - 4)$$