1. The problem asks to describe the function $g(x)$ in terms of $f(x)$ after applying transformations: a vertical stretch by a factor of 4, a shift to the right by 6 units, and a shift upward by 8 units. 2. The general transformation formula is: $$g(x) = A f(x + B) + C$$ where: - $A$ is the vertical stretch factor. - $B$ controls horizontal shifts (note the sign inside the parentheses). - $C$ controls vertical shifts. 3. Applying the vertical stretch by 4 means $A = 4$. 4. Shifting the graph to the right by 6 units means replacing $x$ by $x - 6$, so inside the function we have $x + B = x - 6$, which gives $B = -6$. 5. Shifting the graph upward by 8 units means adding 8 outside the function, so $C = 8$. 6. Therefore, the function is: $$g(x) = 4 f(x - 6) + 8$$ Final answer: $A = 4$, $B = -6$, $C = 8$