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# 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}right|}-{4} b) Find the sequence of transformation from f to g. Given information: f{{left({x}right)}}={left[{x}right]} c) To sketch the graph of g. Given information: g{{left({x}right)}}=-{2}{left|{x}-{1}right|}-{4} d) To write g in terms of f. Given information: g{{left({x}right)}}=-{2}{left|{x}-{1}right|}-{4}{quadtext{and}quad} f{{left({x}right)}}={left[{x}right]} # 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}right|}-{4} b) Find the sequence of transformation from f to g. Given information: f{{left({x}right)}}={left[{x}right]} c) To sketch the graph of g. Given information: g{{left({x}right)}}=-{2}{left|{x}-{1}right|}-{4} d) To write g in terms of f. Given information: g{{left({x}right)}}=-{2}{left|{x}-{1}right|}-{4}{quadtext{and}quad} f{{left({x}right)}}={left[{x}right]}

Question
Transformation properties asked 2021-02-25
Provide answers to all tasks using the information provided.
a) Find the parent function f.
Given Information: $$g{{\left({x}\right)}}=-{2}{\left|{x}-{1}\right|}-{4}$$
b) Find the sequence of transformation from f to g.
Given information: $$f{{\left({x}\right)}}={\left[{x}\right]}$$
c) To sketch the graph of g.
Given information: $$g{{\left({x}\right)}}=-{2}{\left|{x}-{1}\right|}-{4}$$
d) To write g in terms of f.
Given information: $$g{{\left({x}\right)}}=-{2}{\left|{x}-{1}\right|}-{4}{\quad\text{and}\quad} f{{\left({x}\right)}}={\left[{x}\right]}$$

## Answers (1) 2021-02-26
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
$$g{{\left({x}\right)}}=-{2}{\left|{x}-{1}\right|}-{4},\ \text{the parent function is}\ f{{\left({x}\right)}}={\left[{x}\right]}.$$
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 $$g{{\left({x}\right)}}=-{2}{\left|{x}-{1}\right|}-{4}$$ 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 $$g{{\left({x}\right)}}=-{2}{\left|{x}-{1}\right|}-{4}$$ d)
Multiply $$f (x)\ \by\ -2$$ and then subtract from the parent function to get g(x) in terms of f(x).

### Relevant Questions asked 2021-02-08
a) Find the sequence of transformation from f to g
Given information: $$g{{\left({x}\right)}}=\frac{1}{{2}}{\left|{x}-{2}\right|}-{3}{\quad\text{and}\quad} f{{\left({x}\right)}}={x}^{3}$$
b) To sketch the graph of g.
Given information: $$f{{\left({x}\right)}}={\left|{x}\right|}$$
c) To write g in terms of f.
Given information: $$g{{\left({x}\right)}}=\frac{1}{{2}}{\left|{x}-{2}\right|}-{3}{\quad\text{and}\quad} f{{\left({x}\right)}}={\left|{x}\right|}$$ asked 2021-01-10
g is related to one of the six parent functions.
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b) Describe the sequence of transformations from f to g.
c) Sketch the graph of g by hand.
d) Use function notation to write g in terms of the parent function f.
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a. List a rearranged order of the five traditional stages of the RISC pipeline that will support register-memory operations implemented exclusively by register indirect addressing.
b. Describe what new forwarding paths are needed for the rearranged pipeline by stating the source, destination, and information transferred on each needed new path.
c. For the reordered stages of the RISC pipeline, what new data hazards are created by this addressing mode? Give an instruction sequence illustrating each new hazard.
d. List all of the ways that the RISC pipeline with register-memory ALU operations can have a different instruction count for a given program than the original RISC pipeline. Give a pair of specific instruction sequences, one for the original pipeline and one for the rearranged pipeline, to illustrate each way.
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b) To find: the relationship between im $$(A^{T})$$ and ker (A).
c) To find: the relationship between ker(A) and solution set S
d) To find vecx_0 at the intersection of $${k}{e}{r}{\left({A}\right)}{\quad\text{and}\quad}{\left({k}{e}{r}{A}\right)}^{\bot}$$
e) To find: the lengths of $$\vec{{x}}_{{0}}$$ compared to the other vectors in S asked 2021-05-05
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(a) What is thedensity for X? Sketch a graph of the density function. Indicate onthis graph the probability that X lies between 1.1 and 1.9. Findthis probability.
(b) Find the probability that arandomly selected sample of Pima clay loam will have bulk densityless than $$\displaystyle{0.9}\frac{{g}}{{c}}{m}^{{3}}$$.
(c) Would you be surprised if a randomly selected sample of this type of soil has a bulkdensity in excess of $$\displaystyle{2.0}\frac{{g}}{{c}}{m}^{{3}}$$? Explain, based on theprobability of this occurring.
(d) What point has the property that only 10% of the soil samples have bulk density this high orhigher?
(e) What is the moment generating function for X? asked 2021-03-12
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c)The range of the function $$g{{\left({x}\right)}}={2}^{{{x}-{4}}}$$ in the interval notation.
d)The equation of the asymptote of the function $$g{{\left({x}\right)}}={2}^{{{x}-{4}}}.$$ asked 2021-01-10
Let T be a linear transformation from $$P_{2}\ \text{into}\ P_{2}$$ such that
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Find $${T}{\left({2}-{6}{x}+{x}^{2}\right)}$$ asked 2021-01-27
h is related to one of the six parent functions.
a) Identify the parent function f.
b) Describe the sequence of transformations from f to h.
c) Sketch the graph of h by hand.
d) Use function notation to write h in terms of the parent function f.
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Consider the curves in the first quadrant that have equationsy=Aexp(7x), where A is a positive constant. Different valuesof A give different curves. The curves form a family,F. Let P=(6,6). Let C be the number of the family Fthat goes through P.
A. Let y=f(x) be the equation of C. Find f(x).
B. Find the slope at P of the tangent to C.
C. A curve D is a perpendicular to C at P. What is the slope of thetangent to D at the point P?
D. Give a formula g(y) for the slope at (x,y) of the member of Fthat goes through (x,y). The formula should not involve A orx.
E. A curve which at each of its points is perpendicular to themember of the family F that goes through that point is called anorthogonal trajectory of F. Each orthogonal trajectory to Fsatisfies the differential equation dy/dx = -1/g(y), where g(y) isthe answer to part D.
Find a function of h(y) such that x=h(y) is the equation of theorthogonal trajectory to F that passes through the point P.
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