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23 votes
23 votes
How does g(x)=|x-3| -8 compare to its parent function, f(x)=|x|

User Miguelao
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1 Answer

13 votes
13 votes

Given the function g(x) defined as:


g\mleft(x\mright)=\left|x-3\right|-8

We can go from the parent function f(x) = |x| if we perform the following transformations:


\begin{gathered} 1.)\text{ }f\mleft(x\mright)\rightarrow f\mleft(x\mright)-8 \\ 2.)\text{ }f\mleft(x\mright)\rightarrow f\mleft(x-3\mright) \end{gathered}

Transformation 1.) is a shift of 8 units down and the transformation 2.) is a shift of 3 units to the right. Then, the graph of g(x) is shifted 8 units down and 3 units right from the graph of f(x).

User Apri
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