Questions: Find g(x), where g(x) is the translation 1 unit down of f(x) = 3(x-6)^2 - 4.

Transcript text: Find $g(x)$, where $g(x)$ is the translation 1 unit down of $f(x)=3(x-6)^{2}-4$.

Solution

Solution Steps

To find $ g(x) $, which is the translation of $ f(x) = 3(x-6)^2 - 4 $ 1 unit down, we need to subtract 1 from the constant term of $ f(x) $. This is because translating a function vertically involves adjusting the constant term.

Step 1: Identify the Original Function

The original function is given by: \[ f(x) = 3(x-6)^2 - 4 \]

Step 2: Determine the Translation

We need to translate the function 1 unit down. This involves subtracting 1 from the constant term of the function.

Step 3: Calculate the New Constant Term

The original constant term is $-4$. Subtracting 1 from this gives: \[ -4 - 1 = -5 \]

Step 4: Formulate the Translated Function

The translated function $ g(x) $ is: \[ g(x) = 3(x-6)^2 - 5 \]

Final Answer

The function $ g(x) $ after translating 1 unit down is: \[ \boxed{g(x) = 3(x-6)^2 - 5} \]

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