Suppose that f(x) = x3 and g(x) = -2x3 - 7. which statement best compares the graph of g(x) with the graph of f(x)?

As per the statement given that and

⇒ Let the parent function be

Vertically Stretch: If y =f(x) , then y = a f(x) gives a vertical stretch if a> 1.

Rotation about x -axis:

Shifting down: To shift a graph down some units c, we will be subtracting outside the function:  y= f(x)-c.

Just Multiplying the parent function by 2 means you are stretching it vertically,

i,e  F(x) =

adding the minus sign means you are flipping or rotating it about the x-axis

i,e  

and subtracting 7 means you are moving it down by 7 units

=G(x)

Therefore, the statement best compare the graph G(x) with the graph of F(x)

the graph of G(x) is the graph of F(x) stretched vertically by 2 units,  flipped over the x-axis, and shifted 7 units down.

the correct answer is the second option

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