Question

select all that apply. subtraction of three from the absolute value multiplication of (-1) with the absolute value quantity subtraction of two from the variable inside the absolute value bars multiplication of (-1) with the variable inside the absolute value subtraction of three from the variable inside the absolute value addition of two to the absolute value

Explanation:

1. First, identify the parent absolute value function $y=|x|$, which has a vertex at $(0,0)$ and opens upward.
2. The given graph has a vertex at $(0,-3)$ and opens downward.
3. Reflecting $y=|x|$ over the x-axis (opening downward) gives $y=-|x|$, which corresponds to multiplication of $-1$ with the absolute value quantity.
4. Shifting $y=-|x|$ down 3 units gives $y=-|x|-3$, which corresponds to subtraction of three from the absolute value.
5. The other options do not match the transformations seen in the graph: the vertex's x-coordinate is 0, so there is no horizontal shift (ruling out options modifying the variable inside the absolute value), and the graph shifts downward, not upward (ruling out addition to the absolute value).

Answer:

• ✅ Subtraction of three from the absolute value
• ✅ Multiplication of $-1$ with the absolute value quantity