Find g(x), where g(x) is the translation 6 units left of f(x)=(x–9)2+1.
Question
Find g(x), where g(x) is the translation 6 units left of f(x)=(x–9)2+1.
Solution
To find the function g(x) which is the translation 6 units left of f(x) = (x–9)² + 1, you need to replace every x in f(x) with (x+6). This is because moving a function to the left on a graph involves adding to the x-values.
So, g(x) = ((x+6)–9)² + 1 simplifies to g(x) = (x-3)² + 1.
Therefore, g(x) = (x-3)² + 1 is the function that is 6 units to the left of f(x) = (x–9)² + 1.
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