Question

which function is graphed?
$f(x) = |x - 5| + 5$
$f(x) = |x| + 5$
$f(x) = |x - 5|$
$f(x) = 2|x - 5|$

Explanation:

Step1: Identify vertex of parent function

The parent absolute value function is $f(x)=|x|$, with vertex at $(0,0)$.

Step2: Locate graphed function's vertex

From the graph, the vertex is at $(5,0)$.

Step3: Match vertex to transformation

For $f(x)=|x-h|+k$, vertex is $(h,k)$. Here $h=5, k=0$, so $f(x)=|x-5|$.

Step4: Verify slope

The graph has a slope of $\pm1$, matching $f(x)=|x-5|$ (no vertical stretch, unlike $2|x-5|$, and no vertical shift unlike $|x|+5$ or $|x-5|+5$).

Answer:

C. $f(x) = |x - 5|$