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Find g(x) g(x) , where g(x) g(x) is the translation 1 1 unit down of f(x)=∣x∣ f(x) = |x| .\newlineWrite your answer in the form a∣x−h∣+k a|x - h| + k , where a a , h h , and k k are integers.\newlineg(x)= g(x) = ______\newline

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Transformations of absolute value functionsright chevron icon

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Q. Find g(x) g(x) , where g(x) g(x) is the translation 1 1 unit down of f(x)=∣x∣ f(x) = |x| .\newlineWrite your answer in the form a∣x−h∣+k a|x - h| + k , where a a , h h , and k k are integers.\newlineg(x)= g(x) = ______\newline
  1. Understanding downward translation: Understand the effect of translating a function downward.\newlineTranslating a function downward by kk units involves subtracting kk from the function's value. The general form of the translation is g(x)=f(x)−kg(x) = f(x) - k.
  2. Applying the translation to the given function: Apply the translation to the given function.\newlineSince we want to translate f(x)=∣x∣f(x) = |x| one unit down, we set k=1k = 1 and apply the translation to f(x)f(x).\newlineg(x)=f(x)−1g(x) = f(x) - 1\newlineg(x)=∣x∣−1g(x) = |x| - 1
  3. Writing the translated function in required form: Write the translated function in the required form.\newlineThe question asks us to write the answer in the form a∣x−h∣+ka|x - h| + k. Since there is no horizontal translation or reflection, h=0h = 0 and a=1a = 1. The vertical translation is one unit down, so k=−1k = -1.\newlineg(x)=1∣x−0∣−1g(x) = 1|x - 0| - 1

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