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{{ printedBook.courseTrack.name }} {{ printedBook.name }} We are asked to graph the equation $y=-∣x∣$ according to the given transformation. When translating absolute value functions, *vertical* translations occur after the absolute value has been evaluated. This is why they are *outside* the absolute value symbols. Consider the following general equation,
$y=-∣x∣+k $
where $k$ is a real number. The graph of this equation is a vertical translation of $y=-∣x∣$ by $k$ units. Let's start with the graph of $y=-∣x∣.$

In this case, $k$ is equal to $4.$ Since this value is *positive*, the transformation will move the graph of $y=-∣x∣$ *up* by $4.$ As an example, we will translate three points on the line $y=-∣x∣$ up by $4$ units.

Translating each and every point $4$ units up means shifting the entire graph of $y=-∣x∣$ up by $4$ units.