1. **Problem Statement:** We are given the graph of $y = g(x)$ and asked to sketch the curve of $y = 10 - g(4x)$ on the same axes. 2. **Understanding the transformation:** The function $y = 10 - g(4x)$ involves two transformations of $g(x)$: - Horizontal compression by a factor of 4 due to $g(4x)$. - Vertical reflection and shift: $10 - g(4x)$ means we reflect $g(4x)$ about the horizontal axis and then shift it up by 10. 3. **Step-by-step transformations:** - Start with $g(x)$. - Replace $x$ by $4x$ to get $g(4x)$, which compresses the graph horizontally by a factor of 4. - Then compute $-g(4x)$, reflecting the graph vertically. - Finally, add 10 to get $10 - g(4x)$, shifting the graph up by 10. 4. **Effect on key points:** - For example, if $g(x)$ at $x = a$ is $g(a) = b$, then $g(4x)$ at $x = \frac{a}{4}$ is $b$. - So the point $(a, b)$ on $g(x)$ corresponds to $(\frac{a}{4}, b)$ on $g(4x)$. - Then on $10 - g(4x)$, the point becomes $(\frac{a}{4}, 10 - b)$. 5. **Summary:** - Horizontally compress $g(x)$ by 4. - Reflect vertically. - Shift up by 10. This completes the sketch instructions for $y = 10 - g(4x)$ based on the graph of $y = g(x)$.