Question

Function g can be thought of as a translated (shifted) version of f(x) = |x|. What is the equation for g(x) when it is translated 2 units to the right? a) g(x) = |x - 2| b) g(x) = |x + 2| c) g(x) = |x| - 2 d) g(x) = |x| + 2

Answer 1

Function g(x) which is a translated version of f(x) = |x| and shifted 2 units to the right is represented as g(x) = |x - 2|. The correct answer is option a) g(x) = |x - 2|.

Step-by-step explanation:

When we translate a function, we shift its graph either vertically or horizontally. If we have a base function such as f(x) = |x|, any translation of this function can be written by adding or subtracting values from x or from the whole function.

When a function is translated 2 units to the right, it's the x-values in the function that are affected. Specifically, we subtract 2 from each x-value. So, the function f(x) = |x|, when translated 2 units to the right, becomes g(x) = |x - 2|.

Therefore, the correct option for function g(x) in this case is option a) g(x) = |x - 2|.

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