a) Find the sequence of transformation from f to g Given information: g(x)=12|x−2|−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|x−2|−3andf(x)=|x|

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a) Find the sequence of transformation from f to g  Given information: g(x)=12|x−2|−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|x−2|−3andf(x)=|x|

ensojadasH · Accepted Answer

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|x−2|−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|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(x)=12|x−2|−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

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

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