Question

function g can be thought of as a translated (shifted) version of $f(x)=|x|$. what is the equation for $g(x)$? choose 1 answer: a $g(x)=|x - 5|+5$ b $g(x)=|x|+5$ c $g(x)=|x - 5|$ d $g(x)=|x + 5|+5$

Explanation:

Step1: Identify vertex of $f(x)$

The vertex of $f(x)=|x|$ is at $(0,0)$.

Step2: Identify vertex of $g(x)$

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

Step3: Determine vertical shift rule

For a vertical shift up by $k$ units, $g(x)=f(x)+k$. Here $k=5$.

Step4: Write equation for $g(x)$

Substitute $f(x)=|x|$ into the shift rule: $g(x)=|x|+5$.

Answer:

B. $g(x) = |x| + 5$