Answer:
As per the statement given that \(F(x) = x^3\) and \(G(x) = -2x^3-7\)
⇒ Let the parent function be \(F(x) = x^3\)
Vertically Stretch: If y =f(x) , then y = a f(x) gives a vertical stretch if a> 1.
Rotation about x -axis: \((x, y) \rightarrow (x, -y)\)
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) =\(x^3 \rightarrow \text{Vertically stretch by 2} \rightarrow 2x^3\)
adding the minus sign means you are flipping or rotating it about the x-axis
i,e \(2x^3 \rightarrow \text{Rotation about x- axis} \rightarrow -2x^3\)
and subtracting 7 means you are moving it down by 7 units
\(-2x^3 \rightarrow \text{Shifted down by 7 units} \rightarrow -2x^3-7\) =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.