melodykap

2021-02-25

Provide answers to all tasks using the information provided.

a) Find the parent function f.

Given Information:$g\left(x\right)=-2|x-1|-4$

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:$g\left(x\right)=-2|x-1|-4$

d) To write g in terms of f.

Given information:$g\left(x\right)=-2|x-1|-4{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}f\left(x\right)=\left[x\right]$

a) Find the parent function f.

Given Information:

b) Find the sequence of transformation from f to g.

Given information:

c) To sketch the graph of g.

Given information:

d) To write g in terms of f.

Given information:

Gennenzip

Skilled2021-02-26Added 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

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

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

If c is a real number which is also positive, thenthe graph of

2. Horizontal Shift: If c is a real number which is also positive then, the graph of

If c is a real number which is also positive then, the graph of

3. Reflection: The graph for the function say

The graph for the function say

4. Vertical Stretching and Shrinking: If c succ 1 then, the graph of

If 0 prec c prec 1 then, the graph of

5. Horizontal Stretching and Shrinking: If c succ 1 then, the graph of

If 0 prec c prec 1 then, the graph of

The shape of

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

d)

Multiply

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