Question

writing function transformations
the function ( g(x) ), graphed below, is a transformation of the function ( f(x) = |x| ).
write the formula for ( g(x) ).

note: be sure to write your answer using proper function notation. please write ( g(x)= ) at the beginning of your answer. use abs for absolute value. example: ( g(x)=abs(x - 2)-1 )

function:

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Explanation:

Step1: Identify vertex of $f(x)$

The parent function $f(x)=|x|$ has vertex at $(0,0)$.

Step2: Identify vertex of $g(x)$

From the graph, $g(x)$ has vertex at $(2,1)$.

Step3: Apply horizontal/vertical shifts

For vertex $(h,k)$, the form is $|x-h|+k$. Here $h=2, k=1$, so $\text{abs}(x-2)+1$.

Step4: Verify slope/y-intercept

Check $x=0$: $\text{abs}(0-2)+1=3$, which matches the graph's y-intercept of 3.

Answer:

g(x)=abs(x-2)+1