The absolute value function is the function;
[tex]y=|x|[/tex]STEP 1: To stretch this function vertically by a factor of 2 would mean multiplying the function by 2, we have as a result;
[tex]y=2|x|[/tex]STEP 2: To reflect the function over the x-axis, this means that the entire function is multiplied by a negative sign, we have as a result;
[tex]y=-2|x|[/tex]STEP 3: To shift a function horizontally by 6 units to the right means subtracting 6 from every x- value. we have as a final result;
[tex]y=-2|x-6|[/tex]Therefore, the equation of an absolute value function that has been stretched by a factor of 2, reflected across x-axis, and shifted 6 units to the right is;
[tex]y=-2|x-6|[/tex]