Question

Find g(x), where g(x) is the translation 2 units right and 9 units down of f(x)=|x|.

Write your answer in the form a|x–h|+k, where a, h, and k are integers.

Answer 1

g(x) = |x - 2| - 9

Explanation:

Translations of a function f(x):

Translation of f(x) by a units to the right is given by f(x - a).

Translation of f(x) by a units to the left is given by f(x + a).

Translation of f(x) by a units down is f(x) - a

Translation of f(x) by a units up is f(x) + a

Find g(x), where g(x) is the translation 2 units right and 9 units down of f(x)=|x|.

2 units right: f(x - 2) = |x - 2|

9 units down: f(x - 2) - 9 = |x - 2| - 9

The answer is: g(x) = |x - 2| - 9