gutysantillan0205
Answered

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The graph of F(x) can be compressed vertically and shifted to the right to produce the graph of G(x) . If F(x) = x ^ 3 , which of the following could be the equation of G(x) ?

The Graph Of Fx Can Be Compressed Vertically And Shifted To The Right To Produce The Graph Of Gx If Fx X 3 Which Of The Following Could Be The Equation Of Gx class=

Sagot :

Given:

The function is:

[tex]F(x)=x^3[/tex]

To find:

The function G(x) if the graph of F(x) can be compressed vertically and shifted to the right to produce the graph of G(x).

Solution:

The transformation is defined as

[tex]g(x)=kf(x+a)+b[/tex]                .... (i)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

It is given that F(x) can be compressed vertically and shifted to the right to produce the graph of G(x). So, the value of k must be lies between 0 and 1, and a<0.

In option A, [tex]0<k<1[/tex] and [tex]a<0[/tex]. So, this option is correct.

In option B, [tex]0<k<1[/tex] and [tex]a>0[/tex]. So, this option is incorrect.

In option C, [tex]k>1[/tex] and [tex]a>0[/tex]. So, this option is incorrect.

In option D, [tex]k>1[/tex] and [tex]a<0[/tex]. So, this option is incorrect.

Therefore, the correct option is A.

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