Jaden Easton

2021-02-08

a) Find the sequence of transformation from f to g

Given information:$g\left(x\right)=\frac{1}{2}|x-2|-3{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}f\left(x\right)={x}^{3}$

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:$g\left(x\right)=\frac{1}{2}|x-2|-3{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}f\left(x\right)=\left|x\right|$

Given information:

b) To sketch the graph of g.

Given information:

c) To write g in terms of f.

Given information:

ensojadasH

Skilled2021-02-09Added 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$f\left(x\right)+c\text{}\text{is the graph of}\text{}y=f(x)$ shifted upward by c units.

If c is a real number which is also positive, thenthe graph of$f(x)\text{}-\text{}c\text{}\text{is the graph of}y=(x)$ shifted downwards by c units.

2. Horizontal Shift: If c is a real number which is also positive then, the graph of$f(x\text{}+\text{}c)\text{}\text{is the graph of}y=f(x)$ shifted left by c units.

If c is a real number which is also positive then, the graph of$f(x\text{}-\text{}c)\text{}\text{is the graph of}y=f(x)$ shifted right by c units.

3. Reflection: The graph for the function say$y=f(-x)\text{}\text{is the graph of}y=f(x)$ is the reflection in y-axis.

The graph for the function say$y=\text{}-f(x)\text{}\text{is the graph of}y=f(x)$ is the reflection in x-axis.

4. Vertical Stretching and Shrinking: If c succ 1 then, the graph of$y=cf(x)\text{}\text{is the graph of}\text{}y=f(x)$ stretched vertically by c units.

If 0 prec c prec 1 then, the graph of$y=cf(x)\text{}\text{is nothing but the graph of}\text{}y=f(x)$ shrunk vertically by c units.

5. Horizontal Stretching and Shrinking: If c succ 1 then, the graph of$y=cf(x)\text{}\text{is nothing but the graph of}\text{}y=f(x)$ shrunk horizontally by c units.

If 0 prec c prec 1 then, the graph of$y=cf(x)\text{}\text{is nothing but the graph of}\text{}y=f(x)$ 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$g\left(x\right)=\frac{1}{2}|x-2|-3\text{}\text{is drawn reflected in the x-axis and then stretched by}\text{}\frac{1}{2}$ units and then shifted downward by 3 units.

b)

$g\left(x\right)=\frac{1}{2}|x-2|-3$

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$g\left(x\right)=\frac{1}{2}|x-2|-3$

$g\left(x\right)=\frac{1}{2}f\left(x\right)-3$

c)

Multiply$f(x)\text{}\text{by}\text{}1/2$ and then substract 3 from it to get g(x) in terms of f(x).

$g\left(x\right)=\frac{1}{2}f\left(x\right)-3$

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

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

b)

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

c)

Multiply

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