Question

what transformations were performed on the absolute value parent function to result in this image?
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:

Step1: Identify parent function

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

Step2: Analyze vertical shift

The graph's vertex is at $(0,-3)$, so the parent function is shifted down 3 units. This corresponds to $f(x)=|x|-3$, which is subtraction of 3 from the absolute value.

Step3: Analyze reflection

The graph opens downward, meaning the parent function is reflected over the x-axis. This corresponds to multiplying the absolute value quantity by $-1$, giving $f(x)=-|x|-3$.

Step4: Eliminate other options

No horizontal shift exists (vertex is on the y-axis), so options modifying the inside of the absolute value are invalid. Addition to the absolute value would shift upward, which does not match the graph.

Answer:

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