Question

write an absolute value function given the following transformations.reflection across the x-axisvertical shift 2 units righthorizontal shift 7 units down$y = -|x - 2| + 7$$y = -|x + 2| - 7$$y = -|x - 2| - 7$$y = |x - 2| - 7$

Explanation:

Step1: Start with parent function

The parent absolute value function is $y=|x|$.

Step2: Apply x-axis reflection

Multiply by -1: $y=-|x|$.

Step3: Shift 2 units right

Replace $x$ with $x-2$: $y=-|x-2|$.

Step4: Shift 7 units down

Subtract 7 from the function: $y=-|x-2|-7$.

Answer:

C. $y = -|x - 2| - 7$