Question

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

Answer 1

The correct option is C.

Explanation:

The given function is

`F(x)=x^2`

The transformation of the function is defined as

`G(x)=kF(x)`

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).

`G(x)=-kF(x)`

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.

`G(x)=-4F(x)`

Therefore the correct option is C.

Answer 2

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.