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

melodykap 2021-02-25 Answered
Provide answers to all tasks using the information provided.
a) Find the parent function f.
Given Information: g(x)=2|x1|4
b) Find the sequence of transformation from f to g.
Given information: f(x)=[x]
c) To sketch the graph of g.
Given information: g(x)=2|x1|4
d) To write g in terms of f.
Given information: g(x)=2|x1|4andf(x)=[x]
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Expert Answer

Gennenzip
Answered 2021-02-26 Author has 96 answers

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(x)=[x]
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(x)=2|x1|4, the parent function is f(x)=[x].
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 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=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) 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 of y=f(x) shifted right by c units.
3. Reflection: The graph for the function say y=f(x) is the graph of y=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.
The shape of g(x)=2|x1|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(x)=2|x1|4
image
d)
Multiply f(x) by 2 and then subtract from the parent function to get g(x) in terms of f(x).

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