The given transformations, you need to multiply the function by 1/3 for vertical dilation, reflect over the x-axis by negating the function, translate it right 8 by replacing x with x - 8, and translate it down 3 by subtracting 3 from the entire function. The final transformed function would be -((1/3)f(x - 8) - 3).
Let's apply these transformations to a generic function f(x).
Vertical dilation by a factor of 1/3: Multiply the function by 1/3. New function: g(x) = (1/3)f(x).
Reflection over the x-axis: Negate the entire function. New function: h(x) = -g(x).
Horizontal translation right 8: Replace x with x - 8. New function: j(x) = h(x - 8).
Vertical translation down 3: Subtract 3 from the entire function. New function: k(x) = j(x) - 3.
So, if you have an original function f(x), the final transformed function k(x) incorporating all these transformations would be: k(x) = -((1/3)f(x - 8) - 3).