Question

a transformation is performed on the function $y = |x|$, which results in the graph shifting upward 3 units. what is the equation for the transformation?
$\circ y = |x| + 3$
$\circ y = |x - 3|$
$\circ y = |x + 3|$
$\circ y = 3|x|$

Explanation:

Step1: Recall vertical shift rule

For a function $f(x)$, shifting upward by $k$ units gives $f(x)+k$.

Step2: Apply rule to $y=|x|$

Here $f(x)=|x|$, $k=3$, so new function is $|x|+3$.

Answer:

$y = |x| + 3$