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

Jaden Easton 2021-02-08 Answered
a) Find the sequence of transformation from f to g
Given information: g(x)=12|x2|3andf(x)=x3
b) To sketch the graph of g.
Given information: f(x)=|x|
c) To write g in terms of f.
Given information: g(x)=12|x2|3andf(x)=|x|
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Expert Answer

ensojadasH
Answered 2021-02-09 Author has 100 answers
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 f(x)+c 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 is the graph ofy=(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) is the graph ofy=f(x) shifted left by c units.
If c is a real number which is also positive then, the graph of f(x  c) is the graph ofy=f(x) shifted right by c units.
3. Reflection: The graph for the function say y=f(x) is the graph ofy=f(x) is the reflection in y-axis.
The graph for the function say y= f(x) is the graph ofy=f(x) is the reflection in x-axis.
4. Vertical Stretching and Shrinking: If c succ 1 then, the graph of y=cf(x) 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) 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) 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) is nothing but the graph of y=f(x) 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 g(x)=12|x2|3 is drawn reflected in the x-axis and then stretched by 12 units and then shifted downward by 3 units.
b)
g(x)=12|x2|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(x)=12|x2|3
g(x)=12f(x)3
c)
Multiply f(x) by 1/2 and then substract 3 from it to get g(x) in terms of f(x).
g(x)=12f(x)3
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