To analyze the transformation that converts the graph of \( f(x) = -3|x - 9| - 10 \) into \( g(x) = -3|x - 9| - 3 \), we can compare the two equations.
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Original function: \[ f(x) = -3|x - 9| - 10 \]
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Transformed function: \[ g(x) = -3|x - 9| - 3 \]
The key differences between these two functions lie in the constant terms.
- In \( f(x) \), the constant term is \(-10\).
- In \( g(x) \), the constant term is \(-3\).
To find the vertical transformation, we note that the change from \(-10\) to \(-3\) means:
\[ -3 - (-10) = -3 + 10 = 7 \]
This indicates that \( g(x) \) is attained by shifting the graph of \( f(x) \) upward by 7 units.
Thus, the correct transformation is translates it 7 units up.