gebra 1
BB.5 Transformations of absolute value functions: translations and reflections 9TC

Find $g(x)$, where $g(x)$ is the translation 4 units down of $f(x)=|x|$. Write your answer in the form $\mathrm{a} \mid \mathrm{x}-\mathrm{hl}+\mathrm{k}$, where $\mathrm{a}, \mathrm{h}$, and $\mathrm{k}$ are integers.
\[
g(x)=|x+0|-4
\]
Submit

Step 1 ：The question is asking for a transformation of the absolute value function \(f(x)=|x|\). The transformation is a translation 4 units down. In the context of functions, a translation down means subtracting a certain value from the function. In this case, we need to subtract 4 from \(f(x)\) to get \(g(x)\).

Step 2 ：The form \(a |x-h|+k\) is just a general form of an absolute value function, where \(a\) is the coefficient of the absolute value (which affects the steepness of the graph), \(h\) is the horizontal shift (which moves the graph left or right), and \(k\) is the vertical shift (which moves the graph up or down).

Step 3 ：In this case, \(a=1\), \(h=0\), and \(k=-4\) because we are moving the graph 4 units down. Therefore, \(g(x)=|x+0|-4\) is the correct transformation of \(f(x)\).

Step 4 ：\(\boxed{g(x)=|x|-4}\) is the final answer.