# a) Find the sequence of transformation from f to g Given information: g{{left({x}right)}}=frac{1}{{2}}{left|{x}-{2}right|}-{3}{quadtext{and}quad} f{{l

a) Find the sequence of transformation from f to g
Given information: $g\left(x\right)=\frac{1}{2}|x-2|-3\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}f\left(x\right)={x}^{3}$
b) To sketch the graph of g.
Given information: $f\left(x\right)=|x|$
c) To write g in terms of f.
Given information: $g\left(x\right)=\frac{1}{2}|x-2|-3\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}f\left(x\right)=|x|$
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a)
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 shifted upward by c units.
If c is a real number which is also positive, thenthe graph of shifted downwards by c units.
2. Horizontal Shift: If c is a real number which is also positive then, the graph of shifted left by c units.
If c is a real number which is also positive then, the graph of shifted right by c units.
3. Reflection: The graph for the function say is the reflection in y-axis.
The graph for the function say is the reflection in x-axis.
4. Vertical Stretching and Shrinking: If c succ 1 then, the graph of stretched vertically by c units.
If 0 prec c prec 1 then, the graph of shrunk vertically by c units.
5. Horizontal Stretching and Shrinking: If c succ 1 then, the graph of shrunk horizontally by c units.
If 0 prec c prec 1 then, the graph of stretched horizontally by c units.
Conclusion:
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.
The shape of units and then shifted downward by 3 units.
b)
$g\left(x\right)=\frac{1}{2}|x-2|-3$
Use parent functions and then move them around the coordinate plane throught various types of shifts and thus write one function in terms of the other.
Conclusion:
Obtain the graph of $g\left(x\right)=\frac{1}{2}|x-2|-3$
$g\left(x\right)=\frac{1}{2}f\left(x\right)-3$
c)
Multiply and then substract 3 from it to get g(x) in terms of f(x).
$g\left(x\right)=\frac{1}{2}f\left(x\right)-3$