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The graph of F(x) can be stretched vertically and flipped over the x-axis to produce the graph of G(x). If F(x) = x2, which of the following could be the equation of G(x)?

A. G(x) = 4x2
B. G(x) = -1/4x2
C. G(x) = -4x2
D. G(x) = 1/4x2

Respuesta :

jcherry99
If it is stretched vertically then the answer is between A and C. What is in front of the x^2 must be greater than 1
In other words if y = ax^2 then a must be greater than 1

If it is flipped over the x axis then the answer is C.

Answer:

The correct option is C.

Step-by-step explanation:

The given function is

[tex]F(x)=x^2[/tex]

The transformation of the function is defined as

[tex]G(x)=kF(x)[/tex]

If k>1, then the graph of function F(x) stretched vertically and If 0<k<1, then the graph of function F(x) compressed vertically.

It is given that the graph of F(x) can be stretched vertically, it means the value of k must be greater than 1.

The graph of F(x) is flipped over the x-axis, so the function G(x) is equal to the negative of k times of F(x).

[tex]G(x)=-kF(x)[/tex]

Where must be greater than 1.

In option 3, G(x) is equal to the negative of 4 times of F(x). Only in this option, there is negative relation between F(x) and g(x) with k>1.

[tex]G(x)=-4F(x)[/tex]

Therefore the correct option is C.

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