1. The problem asks to describe the function $g(x)$ in terms of $f(x)$ after applying three transformations: vertical stretch by 6, shift right by 6 units, and shift upward by 8 units. 2. The general rules for transformations are: - Vertical stretch by a factor $a$: multiply the function by $a$, so $g(x) = a f(x)$. - Horizontal shift right by $h$ units: replace $x$ by $x - h$, so $g(x) = f(x - h)$. - Vertical shift up by $k$ units: add $k$ to the function, so $g(x) = f(x) + k$. 3. Applying these transformations step-by-step: - Start with $f(x)$. - Vertical stretch by 6: $g(x) = 6 f(x)$. - Shift right by 6: replace $x$ by $x - 6$, so $g(x) = 6 f(x - 6)$. - Shift upward by 8: add 8, so $g(x) = 6 f(x - 6) + 8$. 4. Therefore, the function after all transformations is: $$g(x) = 6 f(x - 6) + 8$$ This means the graph of $f(x)$ is stretched vertically by 6 times, moved 6 units to the right, and then moved 8 units up.