Find g(x), where g(x) is the translation 5 units right and 7 units up of f(x)=7|x–3|+10.
Question
Find g(x), where g(x) is the translation 5 units right and 7 units up of
f(x) = 7|x - 3| + 10.
Solution
To find g(x), we need to apply the transformations to the function f(x) = 7|x - 3| + 10.
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Translation 5 units to the right: This means we replace every x in the function with (x - 5). So, f(x) becomes f(x - 5) = 7| (x - 5) - 3 | + 10 = 7| x - 8 | + 10.
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Translation 7 units up: This means we add 7 to the entire function. So, f(x - 5) becomes f(x - 5) + 7 = 7| x - 8 | + 10 + 7 = 7| x - 8 | + 17.
Therefore, g(x) = 7| x - 8 | + 17.
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