Answer :
In the first question, we are given the transformed function
f(x) = - | x | + 1
and we are asked what was the first transformation and the second one of the original expresion f(x) = | x |
The first transformation is the multiplication by -1 of the x-variable, which involves a reflection around the x-axis. and the second transformation is a vertical shiftup in one (1) unit.
Transf 1 : reflection around x-axis
Transf 2: vertical shift in one unit
Second problem.
We are given the transformed function
f(x) = 7 |x - 3| - 4
so the first transformation is the subtraction of "3" from the "x" variable, which involves a horizontal shift to the right in 3 units
the second transformation is the product by 7 outside the absolute value symbol. This accounts for a vertical stretching by a factor of "7".
The last transformation is the subtraction of 4 ate the end. This accounts for a vertical shift of 4 units down.
Transf 1: horizontal shift 3 units to the right
Transf 2: vertical stretching by a factor of 7
Transf 3: vertical shift of 4 units down.