Provide answers to all tasks using the information provided. a) Find the parent function f. Given Information: g{{left({x}right)}}=-{2}{left|{x}-{1}ri

a)
Parent function is the basic function of a family of functions that preserves the definitions, shape of its graph and properties of the entire family.
Parent function used in this question is the absolute value function $f\left(x\right)=\left[x\right]$
To identify the parent function, strip all the arithmetic operations on the function to leave behind one higher order operation in just x.
So, remove the arithmetic operation of multiplication by -1 and then addition of 4 to x and addition of 8 to it from the given funcion to get the parent function.
Conclusion:
So, remove the arithmetic operation of subtractionof 1 from x and multiplication by -2 and then subtraction of g
$g\left(x\right)=-2|x-1|-4,\text{the parent function is}f\left(x\right)=\left[x\right].$
b)
The sequence of transformations from f to g depicts the steps followed and the transformations used to reach from the parent function f to g.
Types of shifts used in function transformation:
1. Vertical shift: If c is a real number which is also positive, then the graph of $f(x)+c\text{is the graph of}y=f(x)$ shifted upward by c units.
If c is a real number which is also positive, thenthe graph of $f(x)-c\text{is the graph of}y=f(x)$ shifted downwards by c units.
2. Horizontal Shift: If c is a real number which is also positive then, the graph of $f(x+c)\text{is the graph of}y=f(x)$ shifted left by c units.
If c is a real number which is also positive then, the graph of $f(x-c)\text{is the graph of}y=f(x)$ shifted right by c units.
3. Reflection: The graph for the function say $y=f(-x)\text{is the graph of}y=f(x)$ is the reflection in y-axis.
The graph for the function say $y=-f(x)\text{is the graph of}y=f(x)$ is the reflection in x-axis.
4. Vertical Stretching and Shrinking: If c succ 1 then, the graph of $y=cf(x)\text{is the graph of}y=f(x)$ stretched vertically by c units.
If 0 prec c prec 1 then, the graph of $y=cf(x)\text{is nothing but the graph of}y=f(x)$ shrunk vertically by c units.
5. Horizontal Stretching and Shrinking: If c succ 1 then, the graph of $y=cf(x)\text{is nothing but the graph of}y=f(x)$ shrunk horizontally by c units.
If 0 prec c prec 1 then, the graph of $y=cf(x)\text{is nothing but the graph of}y=f(x)$ stretched horizontally by c units.
The shape of $g\left(x\right)=-2|x-1|-4$ is drawn reflected in the x-axis and then shifted right by 1 unit and stretched by 2 units and then downward by 4 units.
The sequence of transformations from f to g depicts the steps followed and the transformations used to reach from the parent function f to g.
Conclusion:
The shape of is drawn reflected in the x-axis and then shifted right by 1 unit and stretched by 2 units and then shifted downward by 4 units is the required sequence of transfomations from f to g.
c)
Use the sequence of tranformation to plot the graph of the function.
Obtain the graph of $g\left(x\right)=-2|x-1|-4$

d)
Multiply $f(x)by-2$ and then subtract from the parent function to get g(x) in terms of f(x).