Final answer:
The absolute maximum value is 259, which occurs at x = -3, and the absolute minimum value is -237, which occurs at x = 5.
Step-by-step explanation:
The function $f(x) = 43 - 56x$ is a linear function. To find the absolute maximum and minimum values on the interval [-3, 5], we need to examine the endpoints and critical points.
To find the critical points, we take the derivative of the function and set it equal to zero: $f'(x) = -56$. Since the derivative is constant, there are no critical points within the interval.
Therefore, to find the absolute maximum and minimum values, we evaluate the function at the endpoints: $f(-3) = 43 - 56(-3) = 259$ and $f(5) = 43 - 56(5) = -237$. The absolute maximum value is 259, which occurs at $x = -3$, and the absolute minimum value is -237, which occurs at $x = 5$.